{
  "edition": "public",
  "items": [
    {
      "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."
    }
  ],
  "status": "Scope map, not a claim that every item has an individual interactive control."
}