Scoped exclusion
Irreducible F20 four cannot host independent native family clock
In the question: Common clock sectors, quartic geometry and operational reconstruction
Smallestnecessaryjointclocktestbeforephysicallyequatingseparatelyvalidfour-bridges. NoexclusionofnativeHodge subchannel,separateE8/thetaresults orlargersourcerepresentations. Oldrank8modulefixesarithmeticcommutationbutisnotphysicalsigma realizationwithoutdictionary.
Read the exact result, assumptions and evidence
Result
ActualnativeC5,G versus frozenv634sigma givecommutatorrank4 andbothranksGsigmaG^-1−sigma^±1 equal4. InanyirreducibleF20four,C5 hasfourdistincteigenvalues cyclicallypermutedbyG. Given[C5,sigma]=0 andorder3,G-fixingpermitsonlyscalartraces4,4omega,4omega²;G-inversiononlytraces4 or−2. Nativesigma hastrace1,hencebothimpossible. Originalcyclotomicplusrelationalreadyexists onrationalrank8Q(zeta30),withfamilymultiplicationtrace−4. Thisisnotnativecomplexsigmatrace1. Thetaalpha inversionisyetanotherclocktype.
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.
- Original Pauli and v419 F20 source words
Use frozen v783 two-qubit Clifford generators, existing Pauli16 and central mu8, and actual cyclotomic v419 C5,G matrices. A constructed source-word F20 subgroup is available; its physical seam selection is not assumed.
Original evidence
- NATIVE-F20-JOINT-CLOCK-TYPECHECK.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/NATIVE-F20-JOINT-CLOCK-TYPECHECK.txt
636378eff2bbc119d856bb416fad3bc8ce5adac790cef2ef46c6e225cec07371
- NATIVE-F20-JOINT-CLOCK-TYPECHECK.txt lines 201–211
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/NATIVE-F20-JOINT-CLOCK-TYPECHECK.txt
636378eff2bbc119d856bb416fad3bc8ce5adac790cef2ef46c6e225cec07371
- check_native_f20_joint_clock.py lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/check_native_f20_joint_clock.py
bb219e3eda987571c07161d7e07654b7959c5a6eb8f86e5719f0976dd7b1d46a
- check_native_f20_joint_clock.py lines 201–207
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/check_native_f20_joint_clock.py
bb219e3eda987571c07161d7e07654b7959c5a6eb8f86e5719f0976dd7b1d46a
- native-f20-joint-clock-results.json lines 1–186
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/native-f20-joint-clock-results.json
3d32adb64f3cb03f93f6b2d4c5e79c06d16b3442177937ca7c9e2cce5d73955b
finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock