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feat(numeric): GF ladder expansion v1.2 — closed-form rule normative (+GF6/10/14/48/96/128/256/512/1024) #1051

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Jun 7, 2026
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feat(numeric): GF ladder expansion v1.2 — closed-form rule normative (+GF6/10/14/48/96/128/256/512/1024) #1051

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feat(numeric): GF ladder expansion v1.2 — closed-form rule normative
AgentMedia1942 Jun 7, 2026
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docs(NOW): sync 2026-06-07 -- GF ladder expansion v1.2
AgentMedia1942 Jun 7, 2026
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105 changes: 84 additions & 21 deletions conformance/FORMAT-SPEC-001.json
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{
"format_family": "GoldenFloat",
"version": "1.1",
"canonical_reference": "THM-009 (phi_ratio optimality) — see specs/numeric/phi_ratio.t27 and docs/nona-02-organism/NUMERIC-STANDARD-001.md",
"normative_markdown": "docs/nona-02-organism/NUMERIC-STANDARD-001.md",
"version": "1.2",
"version_history": {
"1.0": "Initial GF4..GF64 (8 rungs)",
"1.1": "GF16 primary marker, phi_identity Ring 45 reference",
"1.2": "Ladder expansion: +GF6, GF10, GF14, GF48, GF96, GF128, GF256, GF512, GF1024, GFTernary, TF3. Closed-form rule promoted to normative. Frozen-silicon anchor recorded."
},
"canonical_reference": "THM-009 (phi_ratio optimality) -- see specs/numeric/phi_ratio.t27 and docs/NUMERIC_FORMATS_SSOT.md",
"normative_markdown": "docs/NUMERIC_FORMATS_SSOT.md",
"value_formula": "(-1)^S * 2^(E - bias) * (1 + M / 2^mant_bits)",
"closed_form_rule": {
"normative": true,
"exp_bits": "e = round((N - 1) / phi^2)",
"mant_bits": "m = N - 1 - e",
"bias": "bias = 2^(e - 1) - 1 for e >= 1",
"exp_max": "exp_max = 2^e - 1",
"applicability": "N >= 4 (binary ladder). N = 2 reserved for GFTernary special case (2-bit code, no E/M split).",
"phi_target": "E/M -> 1/phi ~= 0.6180339887",
"rationale": "Single closed law across the entire 4-to-1024-bit ladder. Anchor identity phi^2 + phi^-2 = 3 = L_2."
},
"phi_identity": {
"theorem": "phi_squared_equals_phi_plus_one",
"statement": "φ² = φ + 1 (exact in f64, Ring 45 proven)",
"statement": "phi^2 = phi + 1 (exact in f64, Ring 45 proven)",
"phi_f64_hex": "0x1.9E3779B97F4A8p+0",
"phi_sq_f64_hex": "0x1.4F1BBCDCBFA54p+1",
"phi_plus_one_f64_hex": "0x1.4F1BBCDCBFA54p+1",
Expand All @@ -16,26 +31,74 @@
"ring_proven": 45,
"reference": "Kernel/Phi.v (L5 IDENTITY proof)"
},
"frozen_silicon_anchor": {
"format": "GF16",
"rtl_path": "gHashTag/tt-trinity-gamma/src/gf16_v2_mul.v",
"tapeout": "TTSKY26b TT4913 Gamma",
"layout_verbatim": "[S(1) | E(6) | M(9)], bias 2^(E-1)-1 = 31",
"verilog_constants": {
"exp_msb_lsb": "[14:9]",
"mant_msb_lsb": "[8:0]",
"EXP_MAX": 63,
"BIAS": 31
},
"rounding_mode": "ties-to-zero (frozen); ties-to-even variant staged in gf16_v3_mul.v",
"rounding_audit": "tt-trinity-corona/docs/GF16_ROUNDING_CONFORMANCE.md"
},
"formats": {
"GF4": { "bits": 4, "sign": 1, "exp": 1, "mant": 2, "bias": 0, "phi_dist": 0.118 },
"GF8": { "bits": 8, "sign": 1, "exp": 3, "mant": 4, "bias": 3, "phi_dist": 0.132 },
"GF12": { "bits": 12, "sign": 1, "exp": 4, "mant": 7, "bias": 7, "phi_dist": 0.047 },
"GF16": {
"bits": 16,
"sign": 1,
"exp": 6,
"mant": 9,
"bias": 31,
"phi_dist": 0.0486326415435630,
"primary": true
"GFTernary": {
"bits": 2, "sign": 1, "exp": 0, "mant": 1, "bias": "N/A", "exp_max": "N/A",
"em_ratio": "N/A", "phi_dist": 0.0,
"rule_status": "special_case",
"claim_status": "Conj",
"note": "2-bit code {-phi, 0, +phi}. phi-distance 0 by construction (the nonzero magnitude IS phi). Not a float-ladder rung.",
"spec": "specs/numeric/gfternary.t27"
},
"GF20": { "bits": 20, "sign": 1, "exp": 7, "mant": 12, "bias": 63, "phi_dist": 0.035 },
"GF24": { "bits": 24, "sign": 1, "exp": 9, "mant": 14, "bias": 255, "phi_dist": 0.025 },
"GF32": { "bits": 32, "sign": 1, "exp": 12, "mant": 19, "bias": 2047, "phi_dist": 0.014 },
"GF64": { "bits": 64, "sign": 1, "exp": 24, "mant": 39, "bias": 8388607, "phi_dist": 0.00265, "extension": true }
"GF4": { "bits": 4, "sign": 1, "exp": 1, "mant": 2, "bias": 0, "exp_max": 1, "em_ratio": 0.500000, "phi_dist": 0.118034, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf4.t27" },
"GF6": { "bits": 6, "sign": 1, "exp": 2, "mant": 3, "bias": 1, "exp_max": 3, "em_ratio": 0.666667, "phi_dist": 0.048633, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf6.t27", "note": "NEW v1.2" },
"GF8": { "bits": 8, "sign": 1, "exp": 3, "mant": 4, "bias": 3, "exp_max": 7, "em_ratio": 0.750000, "phi_dist": 0.131966, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf8.t27" },
"GF10": { "bits": 10, "sign": 1, "exp": 3, "mant": 6, "bias": 3, "exp_max": 7, "em_ratio": 0.500000, "phi_dist": 0.118034, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf10.t27", "note": "NEW v1.2" },
"GF12": { "bits": 12, "sign": 1, "exp": 4, "mant": 7, "bias": 7, "exp_max": 15, "em_ratio": 0.571429, "phi_dist": 0.046605, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf12.t27" },
"GF14": { "bits": 14, "sign": 1, "exp": 5, "mant": 8, "bias": 15, "exp_max": 31, "em_ratio": 0.625000, "phi_dist": 0.006966, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf14.t27", "note": "NEW v1.2" },
"GF16": { "bits": 16, "sign": 1, "exp": 6, "mant": 9, "bias": 31, "exp_max": 63, "em_ratio": 0.666667, "phi_dist": 0.048633, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf16.t27", "primary": true, "phi_bias": 60, "phi_bias_status": "normative_production" },
"GF20": { "bits": 20, "sign": 1, "exp": 7, "mant": 12, "bias": 63, "exp_max": 127, "em_ratio": 0.583333, "phi_dist": 0.034701, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf20.t27" },
"GF24": { "bits": 24, "sign": 1, "exp": 9, "mant": 14, "bias": 255, "exp_max": 511, "em_ratio": 0.642857, "phi_dist": 0.024823, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf24.t27" },
"GF32": { "bits": 32, "sign": 1, "exp": 12, "mant": 19, "bias": 2047, "exp_max": 4095, "em_ratio": 0.631579, "phi_dist": 0.013545, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf32.t27" },
"GF48": { "bits": 48, "sign": 1, "exp": 18, "mant": 29, "bias": 131071, "exp_max": 262143, "em_ratio": 0.620690, "phi_dist": 0.002656, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf48.t27", "note": "NEW v1.2" },
"GF64": { "bits": 64, "sign": 1, "exp": 24, "mant": 39, "bias": 8388607, "exp_max": 16777215, "em_ratio": 0.615385, "phi_dist": 0.002649, "rule_status": "matches", "claim_status": "Verified", "spec": "specs/numeric/gf64.t27", "extension": true, "phi_bias": 8388608, "phi_bias_status": "empirical_coincidence" },
"GF96": { "bits": 96, "sign": 1, "exp": 36, "mant": 59, "bias": 34359738367, "exp_max": 68719476735, "em_ratio": 0.610169, "phi_dist": 0.007864, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf96.t27", "note": "NEW v1.2" },
"GF128": { "bits": 128, "sign": 1, "exp": 49, "mant": 78, "bias": 281474976710655, "exp_max": 562949953421311, "em_ratio": 0.628205, "phi_dist": 0.010171, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf128.t27", "note": "NEW v1.2" },
"GF256": { "bits": 256, "sign": 1, "exp": 97, "mant": 158, "bias": "2^96 - 1", "exp_max": "2^97 - 1", "em_ratio": 0.613924, "phi_dist": 0.004110, "rule_status": "matches", "claim_status": "Conj", "spec": "tt-trinity-gamma/specs/fpga/gf256.t27", "bias_caveat": "stored constant in gamma RTL (~2^71) UNRECONCILED with closed-form 2^96-1; bias OPEN" },
"GF512": { "bits": 512, "sign": 1, "exp": 195, "mant": 316, "bias": "2^194 - 1", "exp_max": "2^195 - 1", "em_ratio": 0.617089, "phi_dist": 0.000945, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf512.t27", "note": "NEW v1.2 (extrapolated; no RTL)" },
"GF1024":{ "bits": 1024,"sign": 1, "exp": 391, "mant": 632, "bias": "2^390 - 1", "exp_max": "2^391 - 1", "em_ratio": 0.618671, "phi_dist": 0.000637, "rule_status": "matches", "claim_status": "Conj", "spec": "specs/numeric/gf1024.t27", "note": "NEW v1.2 (extrapolated; no RTL)" },
"TF3": { "bits": 8, "sign": 1, "exp": 3, "mant": 4, "bias": 3, "exp_max": 7, "em_ratio": 0.750000, "phi_dist": 0.131966, "rule_status": "container", "claim_status": "Conj", "spec": "specs/numeric/tf3.t27", "note": "8-bit ternary-weight container; reuses GF8 1:3:4 geometry. NOT a float-ladder rung." }
},
"phi_bias_policy": {
"status": "empirical per format",
"retracted_closed_form": "PHI_BIAS = EXP_MAX - BIAS reproduces GF64 only; RETRACTED as a general law",
"values": {
"GF4": 0, "GF8": 1, "GF12": 2, "GF16": 60, "GF20": 289, "GF24": 1364, "GF32": 0, "GF64": 8388608
},
"values_open_for_new_rungs": ["GF6", "GF10", "GF14", "GF48", "GF96", "GF128", "GF256", "GF512", "GF1024"],
"fibonacci_lucas_coincidences": "descriptive, NOT prescriptive -- do not use to generate PHI_BIAS for new formats"
},
"sacred_constants": {
"PHI": { "value": 1.6180339887498948482, "tolerance": 1e-15 },
"TRINITY": { "value": 3.0, "tolerance": 0.0 }
}
"TRINITY": { "value": 3.0, "tolerance": 0.0, "identity": "phi^2 + phi^-2 = 3 = L_2 (Lucas)" }
},
"claim_status_legend": {
"Verified": "machine-checked math, our own audit, or faithful transcription of an external standard",
"Conj": "open conjecture; structural claim without proof; carries falsification path",
"Efit": "empirical fit (numeric match, no derivation)",
"Risk": "high-risk (likely to fail external test)",
"Retr": "retracted"
},
"cross_repo_consumers": [
"gHashTag/tt-trinity-gamma -- RTL for GF4..GF256 (frozen silicon for GF16)",
"gHashTag/tt-trinity-corona -- ROM records for all 80 formats; GF cluster routed via D2D to Gamma",
"gHashTag/goldenfloat-preprint -- arXiv cs.AR (Hunhold endorsed, code QFHDTL)",
"gHashTag/arith2027-goldenfloat -- ARITH 2027 submission",
"gHashTag/trinity-s3ai -- Coq proofs, claims.yaml ledger",
"gHashTag/claim-audit-lab -- public self-audit ledger"
]
}
9 changes: 8 additions & 1 deletion docs/NOW.md
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# NOW -- Trinity t27 sync

Last updated: 2026-06-02
Last updated: 2026-06-07

## feat-gf-ladder-expansion-v1.2 -- GF ladder expansion v1.2 closed-form rule + Corona ROM CATALOG fix (Closes #1052)

- **WHERE** (numeric specs + conformance + codegen): `specs/numeric/goldenfloat_family.t27` extended from 9 rungs (GF4..GF256) to 17 binary rungs (GF4..GF1024) using the single closed-form rule `e = round((N-1)/phi^2)`, all field widths verified at 50 digits with mpmath. Nine new per-rung spec files `specs/numeric/gf{6,10,14,48,96,128,256,512,1024}.t27`. `conformance/FORMAT-SPEC-001.json` bumped to v1.2 with `frozen_silicon_anchor` for GF16. `docs/NUMERIC_FORMATS_SSOT.md` updated to 18-rung table (GFTernary + 17 binary + TF3 container). `specs/numeric/formats_catalog.t27` GF128 typo fixed, 8 rule-derived entries added. Corona ROM CATALOG: 8 corrections to broken rung entries in `tools/gen_rom.py` CATALOG cluster 3 (GF16/24/32/48/64/96/128/256), RECORD_COUNT expanded 80->82 for GF512/GF1024.
- **Why**: one closed-form rule `e = round((N-1)/phi^2)` reproduces field widths for all 17 binary rungs (verified arithmetic, not a quality claim). GF128 was emitting wrong field widths (49/78, was 48/79) -- corrected. All new rungs are Conj (no RTL, no external DOI); GF16 stays the only Verified end-to-end rung (FPGA 35/35 @ 323 MHz). PHI_BIAS values per-format remain OPEN. Uniqueness claim softened to epistemic. Companion PRs: tt-trinity-corona PR #3, tt-trinity-gamma PR #118, goldenfloat-preprint PR #2, ARITH PR #1, claim-audit-lab PR #2. L6 gf16 SSOT untouched. Closes #1052.
- **Anchor**: phi^2 + phi^-2 = 3


## funding-json-drips -- add FUNDING.json for Drips Protocol passive donations (Closes #1050)

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