1988 - The H2LR Typing Packet: Flavor Admitted with Quotient Carrier and Chart Lens (WP45)
The brief's sixth work package: assemble the source-derived package (F, K_flavor, O_flavor, <-,->_flavor) and test whether it descends through every equivalence class the flavor problem declares. It does (6/6 gates), and flavor is admitted as a fourth Marici sector - with a specific typing that WP11 forced and WP44 completed.
The admitted package
carrier F = {(Yu, Yd)} / U(3)^3 - the physical flavor quotient lens K = sparse nine-link chart atlas: 9 edge magnitudes per pair + loop U(1) holonomy readout O = observables17: 6 quark masses, 6 |V_ij|, 3 unitarity angles, 2 light-mass ratios pairing <-,-> = the WP44 gap-cancelled law: C_anchor = (block gap) Dd (CKM monomial) / (scale^2 |Hd_02|^2 |Hd_12|)
Gate results (checkers/wp45_h2lr_typing.py, 6/6)
G1 full U(3)^3 quotient: obs17 invariant under random basis change, 1.1e-10 per-coordinate relative. G2 chart groupoid (rephasings + permutations): 6.7e-12. G3 fiber compatibility: charts land inside experimental fibers, max pull 1.60 sigma. G4 CP conjugation: exact (masses/|V| identical, angles reflected). G5 pairing factorization: WP44 law re-verified, n = 394, 2.7e-11. G6 lens vs readout: phi std 19.86 deg vs gamma std 0.13 deg, ratio 152.5.
What the typing settles
- The nine-link graph is NOT the carrier (WP11); it is the lens. The carrier is the physical U(3)^3 quotient, and the sparse textures are its chart atlas.
- phi and the Yukawa triangle are internal lens coordinates; only their CKM image is readout. G6 makes the split quantitative: the lens coordinate is two orders of magnitude more volatile than the readout it feeds.
- The anchor constants are point values through exact chart algebra (WP44), evaluated at the physical flavor point; the pairing is exact on the Hd_01 = 0 family and certified not to extend universally.
- Consequently the pi/8 clustering is lens-level phenomenology. After WP11 + WP45 it cannot be promoted to a physical law except through a pushforward into the weak-basis invariant ring - which remains the one open route (Nima's harmonic-support question) and is explicitly not claimed here.
Methods note (load-bearing for future gates)
Invariance was gated on per-coordinate relative error with masses from a direct SVD of Y. The naive route (eigh on H = Y Y^dagger, absolute comparison) fails G1/G2 at ~3e-6 purely from the eps ||H||/lambda_min conditioning floor on the light masses - an algorithm artifact, not physics. Recorded in flavor-h2lr-typing-packet.md so no future checker rediscovers it as a fake symmetry violation.
Status vs the brief's admission criterion
The criterion asked for a source-derived package whose essential components descend through the appropriate equivalences. Established: carrier descent (G1), chart-groupoid descent (G2), physical fibers (G3), CP (G4), exact pairing (G5), and the lens/readout separation (G6). Flavor is admitted. The remaining cross-sector step - comparing structural operations to the string/scattering/cosmology sectors before any H2S parent-object claim - is a separate work package and per the brief comes only after this packet, which is now in place.
Evidence: research/flavor/checkers/wp45_h2lr_typing.py, research/flavor/results/wp45_h2lr_typing.json, research/flavor/flavor-h2lr-typing-packet.md.