Skip to main content

Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

All six original Hardy inputs generate the full family coefficient algebra

In the question: Automated construction of operator maps and sources

Complete six-input alphabet in the given kinetic NS/Hardy reader; global twist sectors remain distinct. Squares alone only generate an embedded two-by-two block. Coefficient accessibility does not identify physical field/CAR products or select whole Yukawa, coupling mix, state or time. Equal-weight sum cancels by cubic phases, not a universal source no-go. Existing wedge/Clifford/KO consumer applies linearly. Continue original common use without imposing this route as a universal P1 gate. The linear finite R moment image does not replace the global spin/R action or source state. Two jet orderings do not select physical V_adm or reduce the entire origin to endpoint placement. Do not replace original provenance with another conditional Gram comparison. Only labeling Fhat as fixed-cusp deltaHol fails; genuine coupling or insertion remains eligible. Scalar response does not establish original source selection.

Read the exact result, assumptions and evidence

Result

Actual G columns and original R lift force G_a=G Pc^(-a) and the two-leg map Common=P^(1-b)ScalarP^a, preserving the stated kinetic NS/Hardy domain, metric, spin and full graph. All54 entries are computed:42 exact support/eta zeros and12 continuous-root periods. The two oriented triples are (1,omega²,omega)F and (1,omega²,omega)N, F=alphaE02+betaE21,N=-i(alphaE12+betaE20), with actual normal projector. Reverse phase follows exactly from the calibrated period. Independent65digit replay and source review confirm all inputs. F and N together generate all nine matrix units of M3(C), even without separately adjoining identity, with scalar common commutant. In the SAME originally marked Bstar frame, Fhat=alphaM0P0-betaP0M0 and Nhat=-Dsign Fhat Dsign, hence Fhat is the original delta jet at both marked endpoints with actual period weights. The finite moment reader intertwines rawR with Ad(W), W²=-I, retaining only its ±1 moment lines. Actual fixed-D resolvent traces are exactly (alpha-beta)delta²/(y³-delta³) forFhat and i(alpha-beta)y delta/(y³-delta³) forNhat. Twenty-one additional exact root checks confirm these identities. Actual fixed-cusp tangent test gives d(M³)[Fhat]=(alpha-beta)I nonzero. At the same time its cyclic centralization is ((alpha-beta)/3)M0 and original scalar resolvent trace is (alpha-beta)t²/(1-t³), with determinant linear response -delta²(alpha-beta). Independently verified exactly.

Required assumptions

  • Do not identify source types

    Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

  • Unchanged A0* Fuchsian equation and actual C4 clock

    Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.

  • Recovered genus2 cover with retained coefficients

    Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.

  • Relative spin and reference Hardy cable on original three-cover

    Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.

  • All six original induced inputs at the fixed kinetic NS reader

    Evaluate the six existing offdiagonal mu_ab in the original induced NS/Hardy kinetic reader, Phi=0, finite positive ell_NS and half-frequency. Carry actual G_a input and J E^(b-1) output maps, same continuation, metric, spin, both graph faces and normal symbol. Do not identify individual twist lines or assume a physical combination or multiplicative compression of field products.

  • Original hard-holonomy contract with pure closed-triangle trace

    Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.

  • Original closed real delta transport action

    Original EM3 action on its invertible closed epsilon0 branch with real delta, fixed U6 and all three cusps. Use actual common Gbase dictionary U6=diag(M0,-M0) and fixed marked P0. This is not a newly chosen independently projected physical variation.

Original evidence

  • HARDY-BMU-ALL-SIX-INPUT-READER.txt lines 1–174

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HARDY-BMU-ALL-SIX-INPUT-READER.txt

    3f720735fa509cdb982309d9dbeb896250a9eb799d7081426892be3053acd6ff

  • ROOT-ALL-SIX-INDUCED-DOMAIN-AND-ALGEBRA-REVIEW.txt lines 1–79

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ALL-SIX-INDUCED-DOMAIN-AND-ALGEBRA-REVIEW.txt

    a5f1b91ddc7cfdf8f1ca7d12c4d373296dc534ecc588ef1215a693ba136ba310

  • INDEPENDENT-HARDY-BMU-ALL-SIX-HOM-REVIEW.txt lines 1–122

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/INDEPENDENT-HARDY-BMU-ALL-SIX-HOM-REVIEW.txt

    08be476c6be69fd5a4a2abe3a16416d6c54a346b720d23f1860e938ff3457817

  • ROOT-ALL-SIX-ACTUAL-READER-CHECK.json lines 1–168

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ALL-SIX-ACTUAL-READER-CHECK.json

    4b7d12faf3df1a1f31db9409e0c2b01211cc53271500f6bc9d3244bf5c2fdd2a

  • ROOT-ALL-SIX-ACTUAL-READER-CHECK.json lines 169–336

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ALL-SIX-ACTUAL-READER-CHECK.json

    4b7d12faf3df1a1f31db9409e0c2b01211cc53271500f6bc9d3244bf5c2fdd2a

  • ROOT-SIX-READER-HOM-AND-M3-CHECK.json lines 1–40

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SIX-READER-HOM-AND-M3-CHECK.json

    57f689890772a08f623f2dfdd088c89076f14cc6e759b6135a192e6cddae47bb

  • ROOT-TWO-REVERSE-MU10-PERIODS-CHECK.json lines 1–35

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-TWO-REVERSE-MU10-PERIODS-CHECK.json

    ea115b56724840d2242ba8038876272bc8c43867923ee31b15a8d33db16907dc

  • check_all_six_hardy_reader.py lines 1–123

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_all_six_hardy_reader.py

    803af8ae538995516b25a46d668a954e45f17f518102ecec9b2b7ff58901fb64

  • ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt lines 40–146

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt

    3a57907902631b58e0abee61e9a424c3ac03ff7a8fa074cc4d27e3379b406cf3

  • GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt lines 16–29

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/GEOMETRIC-R-SPIN-COLLAR-REVIEW.txt

    f41d9aa53c27d8e167ec82e7692f9367d073b287a157869a2a39a30114dfe164

  • CANONICAL-BRANCHED-SPIN-PULLBACK.txt lines 23–49

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CANONICAL-BRANCHED-SPIN-PULLBACK.txt

    c61a15753a64da286cef464067e221860cda9495f6efa61082bd39398606d5c3

  • FUCHS-FRAME-INDEPENDENT-TRACE-REVIEW.txt lines 37–100

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FUCHS-FRAME-INDEPENDENT-TRACE-REVIEW.txt

    b6014bc7ff48a743dd62768e66e307b33e552b95829afeb06355cd5381c690a1

  • INDUCED-HARDY-DEFECT-BMU-FINITE-READER.txt lines 18–102

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/INDUCED-HARDY-DEFECT-BMU-FINITE-READER.txt

    209e29b96e4f43d7a4211f3a0a8ccaa0e4607db9991947b622ee174fceb510d3

  • HARDY-BMU-FULL-MU01-READER.txt lines 1–136

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HARDY-BMU-FULL-MU01-READER.txt

    887016f28979a20ba0bfd5c473ed704d253be63ce05656fa9bb9817cb631f17a

  • WHOLE-ALPHABET-ORIGINAL-MARKED-JET-REVIEW.txt lines 1–71

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/WHOLE-ALPHABET-ORIGINAL-MARKED-JET-REVIEW.txt

    41cae8687bfeb928bfbee18788713ca423adb4148ab30947cd3fd24131a9f844

  • ROOT-WHOLE-ALPHABET-MARKED-JET-CHECK.json lines 1–29

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-WHOLE-ALPHABET-MARKED-JET-CHECK.json

    fd5a167224cf74cb2e9280185daed0e29e33512eafaf6ff7a1d73772cb9704e6

  • ROOT-COMMON-MARKED-FUCHS-HARDY-REVIEW.txt lines 1–50

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-COMMON-MARKED-FUCHS-HARDY-REVIEW.txt

    a085f6735da10cafa35e31d9548323d83de628c6ae304cc5ae1c78056fc57bb9

  • ORIGINAL-DELTA-JET-READS-THE-SAME-OPEN-WORD.txt lines 1–130

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-DELTA-JET-READS-THE-SAME-OPEN-WORD.txt

    bf15e9cd8604bbfaf74efd6aec821e53c828ca17fc40ad3d162ea5431f0d58fd

  • ORIGINAL-V118-CUSP-AND-FULL-CONSUMER-REVIEW.txt lines 1–133

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-V118-CUSP-AND-FULL-CONSUMER-REVIEW.txt

    b0f2508190c0a954d807392509de89b833d692e1c168a79c0a0138e996cb6f22

  • ROOT-FIXED-CUSP-TANGENT-CHECK.json lines 1–10

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-FIXED-CUSP-TANGENT-CHECK.json

    08867a4269ba3dec94dc907ce09ac6f2213bccadb2baec6cf37ac5b0e7af0852

finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra