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Q4","actions":[["A",5],["R",-1],["A",-4],["R",2],["A",-2],["R",-1],["U",-1],["R",-1],["A",-1],["R",1],["U",2],["R",-1],["A",-1],["R",1],["U",-1],["B",1],["R",1],["B",2],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-2],["R",-1],["B",1],["R",1],["U",2],["R",-1],["B",1],["R",1],["U",-1],["S",2],["R",1]]},{"label":"Q2 -> Q2","actions":[]},{"label":"Q3 -> P1","actions":[["A",-1],["R",-1],["A",1],["R",2],["A",-1],["R",-1],["B",-1],["R",-1],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q3 -> P2","actions":[["R",-1],["A",1],["R",2],["A",-1],["R",-1],["B",-1],["R",-1],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q3 -> P3","actions":[["A",-1],["R",-1],["A",1],["R",2],["A",-1],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q3 -> P4","actions":[["A",1],["R",-1],["A",1],["R",2],["A",-1],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q3 -> P5","actions":[["R",-1],["A",1],["R",2],["A",-1],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q3 -> Q1","actions":[["A",-5],["R",-1],["A",5],["R",2],["A",2],["R",-1],["U",-1],["R",-1],["A",1],["R",1],["U",2],["R",-1],["A",1],["R",1],["U",-1],["B",-1],["R",1],["B",-2],["R",-2],["U",-1],["B",-1],["U",2],["B",-1],["U",-2],["R",-1],["B",-1],["R",1],["U",2],["R",-1],["B",-1],["R",1],["U",-1],["S",-2],["R",1]]},{"label":"Q3 -> Q3","actions":[]},{"label":"Q3 -> Q4","actions":[["R",-1],["A",1],["R",1]]},{"label":"Q4 -> P1","actions":[["A",-1],["R",1],["A",-1],["R",-1],["B",-1],["R",-1],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q4 -> P2","actions":[["R",1],["A",-1],["R",-1],["B",-1],["R",-1],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q4 -> P3","actions":[["A",-1],["R",1],["A",-1],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q4 -> P4","actions":[["A",1],["R",1],["A",-1],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q4 -> P5","actions":[["R",1],["A",-1],["R",-2],["U",-1],["B",1],["U",2],["B",1],["U",-1],["R",1],["S",-1],["M",-1]]},{"label":"Q4 -> Q1","actions":[["A",-5],["R",-1],["A",4],["R",2],["A",2],["R",-1],["U",-1],["R",-1],["A",1],["R",1],["U",2],["R",-1],["A",1],["R",1],["U",-1],["B",-1],["R",1],["B",-2],["R",-2],["U",-1],["B",-1],["U",2],["B",-1],["U",-2],["R",-1],["B",-1],["R",1],["U",2],["R",-1],["B",-1],["R",1],["U",-1],["S",-2],["R",1]]},{"label":"Q4 -> Q3","actions":[["R",-1],["A",-1],["R",1]]},{"label":"Q4 -> Q4","actions":[]},{"label":"Q5 -> Q5","actions":[]},{"label":"Q5 -> Q6","actions":[["R",-1],["A",1],["R",1]]},{"label":"Q6 -> Q5","actions":[["R",-1],["A",-1],["R",1]]},{"label":"Q6 -> Q6","actions":[]},{"label":"P5 -> Q1","actions":[["A",-1],["R",-1],["A",2],["R",1],["U",-1],["R",-1],["A",1],["R",1],["U",2],["R",-1],["A",1],["R",1],["U",-1],["B",-1],["U",-1],["B",-1],["U",2],["B",-1],["R",1],["B",-1],["R",-1],["U",-1],["R",-1],["U",-1],["R",-1],["B",-1],["R",1],["U",1],["R",1],["U",-1],["R",1],["U",-1],["B",-1],["U",2],["B",-1],["U",-1],["R",-1],["U",2],["R",1],["U",1],["B",-1],["U",-1],["R",-1],["U",-1],["R",-1],["U",1],["R",-1],["U",-1],["B",-1],["U",1],["R",1],["U",-1],["R",2],["S",-1],["R",-1],["M",1]]},{"label":"P5 -> Q3","actions":[["R",-1],["A",-1],["R",2],["A",1],["R",-2],["U",-1],["B",-1],["U",2],["B",-1],["U",-1],["R",1],["S",1],["M",1]]},{"label":"Q5 -> Q6","actions":[["R",-1],["A",1],["R",1]]},{"label":"P5 -> F01(k=8), n=-6","actions":[["A",-4],["R",-1],["A",7],["R",2],["A",1],["R",-1],["U",-1],["R",-1],["A",2],["R",1],["U",2],["R",-1],["A",2],["R",1],["U",-1],["B",-2],["R",-1],["B",1],["R",2],["B",1],["R",-1],["U",-1],["B",-2],["U",2],["B",-2],["U",-1],["R",-1],["U",-1],["B",1],["U",2],["B",1],["U",-2],["R",-1],["B",-1],["R",1],["U",1],["R",2],["U",-1],["R",-1],["B",-1],["R",1],["U",1],["R",-2],["U",1],["R",-1],["B",-1],["R",1],["U",-1],["R",2],["U",1],["R",-1],["B",-1],["R",1],["U",-1],["R",-1],["S",1],["M",2]]}],"modelFingerprint":"fb41fb477ded2939ec29c2db8bca39f08a459cf90188d70618acf918258e4206","reports":[],"directories":[],"coverageMap":[{"id":"01","subject":"Literal nine-position figure","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--01.json","live_scope":"Private context only; not distributed."},{"id":"02","subject":"Rhombus, hinge and asymmetry","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--02.json","live_scope":"Private context only; not distributed."},{"id":"03","subject":"Whole multiset polarity","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--03.json","live_scope":"Private context only; not distributed."},{"id":"04","subject":"n5 and local conditions","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--04.json","live_scope":"Private context only; not distributed."},{"id":"05","subject":"Four ternary addresses","status":"LIVE INSTRUMENT + RECEIPT","detail":"The construction assigns a value to each of81 addresses with four coordinates chosen from\u22121,0,+1.","instrument":"#catalogue","receipt":"proofs--05.json","live_scope":"Inspect every value and address in the catalogue."},{"id":"06","subject":"Complete balance space","status":"LIVE INSTRUMENT + RECEIPT","detail":"The declared balance space has eight independent centered ingredients plus an arbitrary mean.","instrument":"#construction","receipt":"proofs--06.json","live_scope":"Choose eight rational coefficients; check all116 line sums and40 opposition pairs."},{"id":"07","subject":"Opposition balance","status":"LIVE INSTRUMENT + RECEIPT","detail":"Opposite addresses sum to twice the field mean.","instrument":"#catalogue","receipt":"proofs--07.json","live_scope":"Inspect a cell and its opposite, and verify all40 distinct pairs."},{"id":"08","subject":"Reader and centre law","status":"LIVE INSTRUMENT + RECEIPT","detail":"Within the adopted completion model, n=9\u03bc\u221251, where \u03bc is the field mean.","instrument":"#catalogue","receipt":"proofs--08.json","live_scope":"Compare the nine centre classes and their means. The reserved extraction key is omitted publicly."},{"id":"09","subject":"Complete real classification","status":"LIVE INSTRUMENT + RECEIPT","detail":"The frozen116-line model and translated observations yield72 affine branches in nine centre classes.","instrument":"#catalogue","receipt":"proofs--09.json","live_scope":"Every branch and arbitrary rational parameter is selectable. The complete classification is a previously reviewed result."},{"id":"10","subject":"Positive, zero, signed and integer strata","status":"LIVE INSTRUMENT + RECEIPT","detail":"Positivity, nonnegativity and integrality impose different restrictions on the continuous branches.","instrument":"#catalogue","receipt":"proofs--10.json","live_scope":"Enter negative, zero and fractional parameters; inspect minima, zeros and integer counts."},{"id":"11","subject":"Reader geometry versus number specificity","status":"REVIEWED RECEIPT","detail":"The reading geometry and numerical specificity were tested separately with shuffled controls.","instrument":null,"receipt":"proofs--11.json","live_scope":"Historical controls are retained as a reviewed result; this Space does not rerun the exhaustive shuffle study."},{"id":"12","subject":"Five P states and two placements","status":"LIVE INSTRUMENT + RECEIPT","detail":"Five strictly positive integer P preparations occur at mean7 and centre12, on two ordered placements.","instrument":"#catalogue","receipt":"proofs--12.json","live_scope":"Load all five generated fields. Public gold supports omit extraction order."},{"id":"13","subject":"P5 representative","status":"LIVE INSTRUMENT + RECEIPT","detail":"P5 is the arithmetic midpoint of P3 and P4 in the complete81-cell field.","instrument":"#catalogue","receipt":"proofs--13.json","live_scope":"Inspect P3, P5 and P4 and the shared A direction. A midpoint is not an elemental assignment."},{"id":"14","subject":"A pattern and sparse invisibility","status":"LIVE INSTRUMENT + RECEIPT","detail":"A changes54 addresses and leaves27 fixed. On the held P placements it leaves the selected observations unchanged.","instrument":"#modes","receipt":"proofs--14.json","live_scope":"Add arbitrary rational multiples of A and inspect the entire field and gold support."},{"id":"15","subject":"Six Q states","status":"LIVE INSTRUMENT + RECEIPT","detail":"Six strictly positive integer Q preparations occur at mean6 and centre3.","instrument":"#catalogue","receipt":"proofs--15.json","live_scope":"Load all six generated fields and compare their ranges, support and admission."},{"id":"16","subject":"120-degree action","status":"LIVE INSTRUMENT + RECEIPT","detail":"The held address action R has order three. A passive reframe carries the observation support and reference inversely.","instrument":"#workbench","receipt":"proofs--16.json","live_scope":"Run R, R\u00b2 and R\u00b3 and inspect complete state restoration."},{"id":"17","subject":"Unique common channel","status":"REVIEWED RECEIPT","detail":"Under the held balance constraints and orientations, A on P and C=RA on Q supply the unique shared one-dimensional channel up to scale.","instrument":null,"receipt":"proofs--17.json","live_scope":"The prepared exchange uses this channel. Its uniqueness proof is a previously reviewed linear-algebra result."},{"id":"18","subject":"Continuous capacities","status":"LIVE INSTRUMENT + RECEIPT","detail":"Each preparation has its own allowed amplitude interval. A shared norm bound a\u00b2+b\u00b2<1/4 is sufficient for the guarded prepared network.","instrument":"#exchange","receipt":"proofs--18.json","live_scope":"Vary amplitudes and inspect exact minima and the common sufficient bound."},{"id":"19","subject":"Reciprocal prepared exchange","status":"LIVE INSTRUMENT + RECEIPT","detail":"Prepared quarter exchange maps(a,b) to(\u2212b,a), preserving the amplitude norm. It does not change the background means.","instrument":"#exchange","receipt":"proofs--19.json","live_scope":"Choose any of30 P/Q pairs; execute quarter turns and inverse turns."},{"id":"20","subject":"Network and resident memory","status":"LIVE INSTRUMENT + RECEIPT","detail":"The prepared exchange network distinguishes traveller return from restoration of resident signals. A four-support loop has an order-three resident action.","instrument":"#network","receipt":"proofs--20.json","live_scope":"Operate one declared four-support loop, three circuits, or its recorded inverse. The full341-route enumeration is historical, not rerun by this control."},{"id":"21","subject":"Phase-aware whole-array conversion","status":"LIVE INSTRUMENT + RECEIPT","detail":"The calibrated conversion maps P5+tA to Q3+tC while retaining t through normalization. Its positive interval is\u22121/2<t<3/2.","instrument":"#conversion","receipt":"proofs--21.json","live_scope":"Inspect six exact stops, the two paired field changes, the mean change and the complete arithmetic return."},{"id":"22","subject":"Original signed backdoor","status":"REVIEWED RECEIPT","detail":"Signed continuation can preserve an observed pattern beyond the positive resting catalogue.","instrument":null,"receipt":"proofs--22.json","live_scope":"The broader signed-state result is retained as reviewed context; no extra positive preparation is inferred."},{"id":"23","subject":"Rhythm and directional memory","status":"REVIEWED RECEIPT","detail":"Matching a period or eigenvalue is weaker than matching phase and orientation.","instrument":null,"receipt":"proofs--23.json","live_scope":"The historical rhythm tests are summarized separately from the live eigenmode and exchange controls."},{"id":"24","subject":"Spectral geometry","status":"LIVE INSTRUMENT + RECEIPT","detail":"The centered balanced fields satisfy Lf=12f for the introduced equal-neighbour cyclic graph. The spectral band is not uniquely PAN-specific.","instrument":"#spectrum","receipt":"proofs--24.json","live_scope":"Test the exact identity at all81 addresses for a catalogue or workbench field; inspect floating-point Fourier magnitudes."},{"id":"25","subject":"Whistle and sonification","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--25.json","live_scope":"Private context only; not distributed."},{"id":"26","subject":"Exact primitive language","status":"LIVE INSTRUMENT + RECEIPT","detail":"Integer A,B,M,R,U,S instructions act on the field, observation support and carried reference.","instrument":"#workbench","receipt":"proofs--26.json","live_scope":"Edit a journal, step or replay it, export a checkpoint and execute its inverse."},{"id":"27","subject":"All-word permission theorem","status":"LIVE INSTRUMENT + RECEIPT","detail":"The recorded instruction language admits an exact joint lattice test rather than only a bounded search.","instrument":"#reach","receipt":"proofs--27.json","live_scope":"Test any two catalogue endpoints. Public admission checks field and unordered support; private admission also checks ordered reading."},{"id":"28","subject":"Three reading phases","status":"REVIEWED RECEIPT","detail":"A residual phase condition distinguishes numerical field reach from joint field-and-reader reach.","instrument":null,"receipt":"proofs--28.json","live_scope":"The ordered phase character remains a reviewed private-key result. The public support test intentionally has a different equivalence relation."},{"id":"29","subject":"Complete branch reach","status":"LIVE INSTRUMENT + RECEIPT","detail":"All5184 ordered branch pairs were classified under the private ordered-reader model:296 admit some parameter pair,928 fail its joint lattice,3960 fail integer mean change.","instrument":"#reach","receipt":"proofs--29.json","live_scope":"Choose arbitrary branch parameters and test endpoints; load recorded admitted words. The complete historical pair enumeration is not recomputed on every click."},{"id":"30","subject":"Negative-centre backdoor","status":"LIVE INSTRUMENT + RECEIPT","detail":"The recorded negative-centre example takes P5 to F01 at k=8 and returns the complete state. Its neighbouring k=9 illustrates an obstruction in the frozen model.","instrument":"#workbench","receipt":"proofs--30.json","live_scope":"Load the actual recorded word and source parameter, then run the inverse. Public support equivalence is labelled separately."},{"id":"31","subject":"Four shared hidden directions","status":"LIVE INSTRUMENT + RECEIPT","detail":"The four recurring D directions are mutually orthogonal, each with squared field length108.","instrument":"#modes","receipt":"proofs--31.json","live_scope":"Add the declared patterns and inspect their81 components and norms."},{"id":"32","subject":"Exact permission lattice","status":"LIVE INSTRUMENT + RECEIPT","detail":"The fixed-reader four-pattern lattice separates geometric length from permitted integer operations.","instrument":"#permission","receipt":"proofs--32.json","live_scope":"Evaluate the exact coordinates in the basis2D1,T,p,q, including every24-cell pair direction at unit and doubled scale."},{"id":"33","subject":"T axis and turning plane","status":"LIVE INSTRUMENT + RECEIPT","detail":"T=(A+RA+R\u00b2A)/3 is fixed by R. The three remainders sum to zero and turn in a triangular plane.","instrument":"#fixed-axis","receipt":"proofs--33.json","live_scope":"Display A,RA,R\u00b2A,their sum3T,the averageT,and R(T); inspect all81 values and the vector decomposition."},{"id":"34","subject":"Shortest changes and visible effects","status":"LIVE INSTRUMENT + RECEIPT","detail":"The shortest nonzero fixed-reader increments are\u00b1T. T can leave the reader arrangement fixed while changing what it reads.","instrument":"#permission","receipt":"proofs--34.json","live_scope":"Add T and compare the gold-support values. A fixed support is not a preserved display."},{"id":"35","subject":"B exceeds four-mode geometry","status":"LIVE INSTRUMENT + RECEIPT","detail":"B has squared norm648: its projection into the four D directions contributes378 and its orthogonal remainder270.","instrument":"#b-residual","receipt":"proofs--35.json","live_scope":"Inspect B,its projection,its remainder,and their exact reconstruction at all81 addresses."},{"id":"36","subject":"Cuboctahedron and24cell","status":"LIVE INSTRUMENT + RECEIPT","detail":"At unit pair scale12 of24 proposed directions are admitted; at doubled scale all24 are admitted. The unit admitted shell is cuboctahedral.","instrument":"#permission","receipt":"proofs--36.json","live_scope":"Select each direction, inspect its integer-lattice certificate and rotate the projection."},{"id":"37","subject":"Two geometrical charts","status":"REVIEWED RECEIPT","detail":"Address projections and directions in field space are different geometric constructions.","instrument":null,"receipt":"proofs--37.json","live_scope":"The separate chart derivations are reviewed context. The viewer labels its analytical geometry."},{"id":"38","subject":"Rhombic floor and hexagram","status":"LIVE INSTRUMENT + RECEIPT","detail":"The floor plane and the T-normal hexagram plane are distinct; their angle is54.7356 degrees.","instrument":"#geometry","receipt":"proofs--38.json","live_scope":"Use the floor,persistence,fourth-direction and solstice scenes. These illustrate the declared metric map, not an absolute physical pose."},{"id":"39","subject":"FCC and diamond extension","status":"REVIEWED RECEIPT","detail":"A tetrahedral address projection yields FCC cosets and a diamond-net extension for specified unwrapped layers. The finite centre choices do not select those layers.","instrument":null,"receipt":"proofs--39.json","live_scope":"The projection and lattice derivation are retained as a reviewed receipt; no interactive infinite-lattice simulator is claimed."},{"id":"40","subject":"Constant-bar contraction","status":"LIVE INSTRUMENT + RECEIPT","detail":"A labelled constant-bar branch contracts a cuboctahedral configuration to six paired sites of an octahedron while preserving the24 bars.","instrument":"#geometry","receipt":"proofs--40.json","live_scope":"Scrub or reverse the labelled contraction scene. The continuous geometry is not an integer instruction word."},{"id":"41","subject":"Tetrahedral continuation","status":"LIVE INSTRUMENT + RECEIPT","detail":"The tetrahedral continuation is an additional explicit twist-and-fold operation beyond the constant-bar branch.","instrument":"#geometry","receipt":"proofs--41.json","live_scope":"Scrub the continuation scene, including the flat triangular net and folded tetrahedron."},{"id":"42","subject":"Three turns create hidden advance","status":"LIVE INSTRUMENT + RECEIPT","detail":"Three repeated mixed changes and R turns restore the carried arrangement while adding2D1 to the field.","instrument":"#mixed-turns","receipt":"proofs--42.json","live_scope":"Execute the actual recorded increment word and R at each stop; compare with the equally rotated starting field and run its inverse."},{"id":"43","subject":"Hidden branch under three turns","status":"LIVE INSTRUMENT + RECEIPT","detail":"The three-turn endpoint preserves the held observations on18 D1 branches while advancing their hidden parameter.","instrument":"#mixed-turns","receipt":"proofs--43.json","live_scope":"Capture a catalogue or workbench state, run the mixed-turn instrument and inspect the full changed field. The18-branch count is a reviewed classification."},{"id":"44","subject":"Location and reference memory","status":"LIVE INSTRUMENT + RECEIPT","detail":"A carried reference is part of the state; restoring an observation support alone does not restore that reference.","instrument":"#workbench","receipt":"proofs--44.json","live_scope":"Watch its address through R,U and inverse instructions."},{"id":"45","subject":"Complete joint return","status":"LIVE INSTRUMENT + RECEIPT","detail":"Full return restores field,observation arrangement and reference. Historical retracing additionally uses the ordered instruction journal.","instrument":"#workbench","receipt":"proofs--45.json","live_scope":"Compare complete states and replay an actual inverse. The public edition restores unordered support; private reading order is separately retained."},{"id":"46","subject":"Facing-compatible information passage","status":"REVIEWED RECEIPT","detail":"A further facing-compatible condition restricts the native joint passages. It is an added analytical rule rather than a star-coordinate derivation.","instrument":null,"receipt":"proofs--46.json","live_scope":"This is a reviewed receipt. The Space does not claim a fresh astronomical facing calculation."},{"id":"47","subject":"Three-symbol packet","status":"REVIEWED RECEIPT","detail":"A three-symbol field encoding has codeword distance54, giving a declared exact decoder a bounded error/erasure capability.","instrument":null,"receipt":"proofs--47.json","live_scope":"This specific packet decoder is a reviewed result, not a live decoder in this release."},{"id":"48","subject":"Coding versus information source","status":"REVIEWED RECEIPT","detail":"Encoding and recovering a supplied payload does not discover an external source of information.","instrument":null,"receipt":"proofs--48.json","live_scope":"The exact-state checkpoint is executable; the broader information-source interpretation remains separate."},{"id":"49","subject":"Stellar frame and ritual orientation","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--49.json","live_scope":"Private context only; not distributed."},{"id":"50","subject":"Exact-state software","status":"LIVE INSTRUMENT + RECEIPT","detail":"A complete state plus replayable instructions supports exact checkpoint,replay and inverse recovery. This does not measure improved LLM performance.","instrument":"#workbench","receipt":"proofs--50.json","live_scope":"Export,restore and verify full state and journal. The separate synthetic software study is linked from the repository."},{"id":"51","subject":"Elemental functions","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--51.json","live_scope":"Private context only; not distributed."},{"id":"52","subject":"Source role and authored continuation","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--52.json","live_scope":"Private context only; not distributed."},{"id":"53","subject":"Red thread source support","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--53.json","live_scope":"Private context only; not distributed."},{"id":"54","subject":"Why active address change matters","status":"LIVE INSTRUMENT + RECEIPT","detail":"An active change of the addressed field differs from a passive reframe that carries its observations along.","instrument":"#workbench","receipt":"proofs--54.json","live_scope":"Compare the active scalar probe with passive R in the workbench."},{"id":"55","subject":"Five-state six-move itinerary","status":"REVIEWED RECEIPT","detail":"The five-state preparation graph has a six-move visiting itinerary under its declared moves. The count is not unique among comparable patches.","instrument":null,"receipt":"proofs--55.json","live_scope":"The itinerary and matched-control enumeration are reviewed receipts; no graph-search interface is claimed here."},{"id":"56","subject":"Measured whistle frequencies","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--56.json","live_scope":"Private context only; not distributed."},{"id":"57","subject":"Counting correspondences as authoredquestions","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--57.json","live_scope":"Private context only; not distributed."},{"id":"58","subject":"Active observation reconstructs hiddenstate","status":"LIVE INSTRUMENT + RECEIPT","detail":"With a known one-parameter family, an active scalar observation can recover its hidden parameter. The fuller known-placement reconstruction was separately tested.","instrument":"#probe","receipt":"proofs--58.json","live_scope":"The live probe tests P5+tA with observed value7+t and exact inversion t=value\u22127. It does not reconstruct an arbitrary unknown81-cell field from one scalar."},{"id":"59","subject":"Calculemicha and computational method","status":"PRIVATE CONTEXT","detail":"Source text or interpretive context remains reserved; this record identifies its boundary.","instrument":null,"receipt":"proofs--59.json","live_scope":"Private context only; not distributed."},{"id":"60","subject":"Quantum, entropy, acoustics and topology boundaries","status":"REVIEWED RECEIPT","detail":"Equal line sums alone establish neither noise cancellation,quantum entanglement,maximum entropy,encryption nor physical transit.","instrument":null,"receipt":"proofs--60.json","live_scope":"The environment tests its stated finite operations and permits declared artistic sonification; the broader applications remain unestablished."},{"id":"61","subject":"Modulo9 as an actual passage invariant","status":"LIVE INSTRUMENT + RECEIPT","detail":"Integer mean-changing instructions preserve the centre modulo9 at valid endpoints because\u0394n=9\u0394\u03bc. This necessary gate is not sufficient for passage.","instrument":"#reach","receipt":"proofs--61.json","live_scope":"Test endpoints with matching and mismatching mean residues and inspect the later field/support lattice gates."}],"edition":"public","catalogue":{"model":"Held 116-line / 81-translated-reader real completion 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RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"07","subject":"Opposition balance","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Opposite addresses sum to twice the field mean.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"08","subject":"Reader and centre law","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Within the adopted completion model, n=9\u03bc\u221251, where \u03bc is the field mean.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"09","subject":"Complete real classification","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The frozen116-line model and translated observations yield72 affine branches in nine centre classes.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"10","subject":"Positive, zero, signed and integer strata","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Positivity, nonnegativity and integrality impose different restrictions on the continuous branches.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"11","subject":"Reader geometry versus number specificity","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The reading geometry and numerical specificity were tested separately with shuffled controls.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"12","subject":"Five P states and two placements","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Five strictly positive integer P preparations occur at mean7 and centre12, on two ordered placements.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"13","subject":"P5 representative","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"P5 is the arithmetic midpoint of P3 and P4 in the complete81-cell field.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"14","subject":"A pattern and sparse invisibility","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A changes54 addresses and leaves27 fixed. On the held P placements it leaves the selected observations unchanged.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"15","subject":"Six Q states","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Six strictly positive integer Q preparations occur at mean6 and centre3.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"16","subject":"120-degree action","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The held address action R has order three. A passive reframe carries the observation support and reference inversely.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"17","subject":"Unique common channel","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Under the held balance constraints and orientations, A on P and C=RA on Q supply the unique shared one-dimensional channel up to scale.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"18","subject":"Continuous capacities","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Each preparation has its own allowed amplitude interval. A shared norm bound a\u00b2+b\u00b2<1/4 is sufficient for the guarded prepared network.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"19","subject":"Reciprocal prepared exchange","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Prepared quarter exchange maps(a,b) to(\u2212b,a), preserving the amplitude norm. It does not change the background means.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"20","subject":"Network and resident memory","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The prepared exchange network distinguishes traveller return from restoration of resident signals. A four-support loop has an order-three resident action.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"21","subject":"Phase-aware whole-array conversion","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The calibrated conversion maps P5+tA to Q3+tC while retaining t through normalization. Its positive interval is\u22121/2<t<3/2.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"22","subject":"Original signed backdoor","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Signed continuation can preserve an observed pattern beyond the positive resting catalogue.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"23","subject":"Rhythm and directional memory","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Matching a period or eigenvalue is weaker than matching phase and orientation.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"24","subject":"Spectral geometry","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The centered balanced fields satisfy Lf=12f for the introduced equal-neighbour cyclic graph. The spectral band is not uniquely PAN-specific.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"25","subject":"Whistle and sonification","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"26","subject":"Exact primitive language","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Integer A,B,M,R,U,S instructions act on the field, observation support and carried reference.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"27","subject":"All-word permission theorem","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The recorded instruction language admits an exact joint lattice test rather than only a bounded search.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"28","subject":"Three reading phases","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A residual phase condition distinguishes numerical field reach from joint field-and-reader reach.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"29","subject":"Complete branch reach","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"All5184 ordered branch pairs were classified under the private ordered-reader model:296 admit some parameter pair,928 fail its joint lattice,3960 fail integer mean change.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"30","subject":"Negative-centre backdoor","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The recorded negative-centre example takes P5 to F01 at k=8 and returns the complete state. Its neighbouring k=9 illustrates an obstruction in the frozen model.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"31","subject":"Four shared hidden directions","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The four recurring D directions are mutually orthogonal, each with squared field length108.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"32","subject":"Exact permission lattice","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The fixed-reader four-pattern lattice separates geometric length from permitted integer operations.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"33","subject":"T axis and turning plane","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"T=(A+RA+R\u00b2A)/3 is fixed by R. The three remainders sum to zero and turn in a triangular plane.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"34","subject":"Shortest changes and visible effects","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The shortest nonzero fixed-reader increments are\u00b1T. T can leave the reader arrangement fixed while changing what it reads.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"35","subject":"B exceeds four-mode geometry","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"B has squared norm648: its projection into the four D directions contributes378 and its orthogonal remainder270.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"36","subject":"Cuboctahedron and24cell","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"At unit pair scale12 of24 proposed directions are admitted; at doubled scale all24 are admitted. The unit admitted shell is cuboctahedral.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"37","subject":"Two geometrical charts","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Address projections and directions in field space are different geometric constructions.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"38","subject":"Rhombic floor and hexagram","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The floor plane and the T-normal hexagram plane are distinct; their angle is54.7356 degrees.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"39","subject":"FCC and diamond extension","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A tetrahedral address projection yields FCC cosets and a diamond-net extension for specified unwrapped layers. The finite centre choices do not select those layers.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"40","subject":"Constant-bar contraction","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A labelled constant-bar branch contracts a cuboctahedral configuration to six paired sites of an octahedron while preserving the24 bars.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"41","subject":"Tetrahedral continuation","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The tetrahedral continuation is an additional explicit twist-and-fold operation beyond the constant-bar branch.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"42","subject":"Three turns create hidden advance","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Three repeated mixed changes and R turns restore the carried arrangement while adding2D1 to the field.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"43","subject":"Hidden branch under three turns","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The three-turn endpoint preserves the held observations on18 D1 branches while advancing their hidden parameter.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"44","subject":"Location and reference memory","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A carried reference is part of the state; restoring an observation support alone does not restore that reference.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"45","subject":"Complete joint return","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Full return restores field,observation arrangement and reference. Historical retracing additionally uses the ordered instruction journal.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"46","subject":"Facing-compatible information passage","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A further facing-compatible condition restricts the native joint passages. It is an added analytical rule rather than a star-coordinate derivation.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"47","subject":"Three-symbol packet","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A three-symbol field encoding has codeword distance54, giving a declared exact decoder a bounded error/erasure capability.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"48","subject":"Coding versus information source","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Encoding and recovering a supplied payload does not discover an external source of information.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"49","subject":"Stellar frame and ritual orientation","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"50","subject":"Exact-state software","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"A complete state plus replayable instructions supports exact checkpoint,replay and inverse recovery. This does not measure improved LLM performance.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"51","subject":"Elemental functions","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"52","subject":"Source role and authored continuation","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"53","subject":"Red thread source support","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"54","subject":"Why active address change matters","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"An active change of the addressed field differs from a passive reframe that carries its observations along.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"55","subject":"Five-state six-move itinerary","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"The five-state preparation graph has a six-move visiting itinerary under its declared moves. The count is not unique among comparable patches.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"56","subject":"Measured whistle frequencies","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"57","subject":"Counting correspondences as authoredquestions","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"58","subject":"Active observation reconstructs hiddenstate","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"With a known one-parameter family, an active scalar observation can recover its hidden parameter. The fuller known-placement reconstruction was separately tested.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"59","subject":"Calculemicha and computational method","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Source text or interpretive context remains reserved; this record identifies its boundary.","formula":"","review_scope":"PRIVATE CONTEXT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"60","subject":"Quantum, entropy, acoustics and topology boundaries","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Equal line sums alone establish neither noise cancellation,quantum entanglement,maximum entropy,encryption nor physical transit.","formula":"","review_scope":"REVIEWED RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]},{"id":"61","subject":"Modulo9 as an actual passage invariant","category":"Public mathematical scope","epistemic_status":"ANALYTICAL CONSTRUCTION","claim":"Integer mean-changing instructions preserve the centre modulo9 at valid endpoints because\u0394n=9\u0394\u03bc. This necessary gate is not sufficient for passage.","formula":"","review_scope":"LIVE INSTRUMENT + RECEIPT","evidence":[],"new_manuscript_chapter_ids":[]}]}