Follow the source behind the result.
Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.
v192_qgeo_energy_clock.py
verification/v192_qgeo_energy_clock.py
This is a registered verification module. Read its original code and the paper sections that cite it, then follow the linked claim to its present classification.
Read the publication code on this page
The registered Python source is shown as text. Displaying it does not execute the code.
"""v192 -- The energy-conserving-clock reformulation of the bedrock (external-review
proposal, point 7), HONESTLY typed: it RELOCATES the bedrock postulate QGEO.SYM.01
to a more operationally checkable operator identity, but does NOT (yet) eliminate
it. The proposed new premise:
QGEO.ENERGY.01: rho^* Lambda_Sigma rho = Lambda_Sigma
(the carrier clock rho preserves the Calderon / Dirichlet-to-Neumann energy
form of the RP seam double)
feeds the EXISTING downstream chain (v180/v181): in 2D, energy preservation =>
conformality; a finite orientation-preserving conformal automorphism on a genus-0
surface is Moebius (Kerekjarto); order 4 => conjugate to z |-> iz; a free 4-orbit
is mu4 -- hence QGEO.SYM.01 (the clock is the seam's conformal deck).
[E] 1. THE DOWNSTREAM CHAIN ALREADY EXISTS. conformality -> Moebius ->
z|->iz -> mu4 -> QGEO.SYM.01 is the v180/v181 reduction (uniformisation,
Kerekjarto, the order-4 Moebius classification), all theorem/citation.
[E] 2. THE PROPOSED UPSTREAM STEP. QGEO.ENERGY.01 (rho preserves Lambda_Sigma)
=> conformality in 2D (Dirichlet-energy invariance is conformal
invariance) is the one new link; it is operator-analytic and checkable on
the DtN operator (= |k|, the rank-8 Calderon polarisation, already in the
net construction), unlike the abstract 'is the conformal deck'.
[O]/[honest] 3. RELOCATES, DOES NOT ELIMINATE. 'rho preserves Lambda_Sigma'
is plausibly EQUIVALENT to 'rho is the conformal deck' (QGEO.SYM.01): in
2D, preserving the DtN energy form IS being a conformal symmetry of the
seam double. So QGEO.ENERGY.01 is a sharper, more checkable RESTATEMENT
of the same bedrock, not a theorem -- UNLESS rho is defined INDEPENDENTLY
(from the carrier algebra) and the invariance is then independently
proven (open). Until then the bedrock stays [O]; the value is a more
falsifiable surface, not a closure. (Same pattern as v179->v181: each
step sharpens/relocates the premise but cannot remove it.)
Python-only (a structural/logical reformulation; no new numeric claim).
"""
import os
import csv
from tfpt_constants import check, summary, reset
HERE = os.path.dirname(os.path.abspath(__file__))
LEDGER = os.path.join(HERE, "status_ledger.csv")
def _ledger_ids():
with open(LEDGER, newline="", encoding="utf-8") as f:
return {r["claim_id"] for r in csv.DictReader(f)}
def run():
reset()
print("v192 energy-conserving clock: QGEO.ENERGY.01 RELOCATES the bedrock (does not eliminate it)")
ids = _ledger_ids()
# 1. the downstream chain already exists in the ledger
chain = ["QGEO.CONF.01", "QGEO.ISO.01", "QGEO.SYM.01"]
have_chain = all(c in ids for c in chain)
check("DOWNSTREAM CHAIN EXISTS [E]: the reduction conformality -> Moebius -> "
"z|->iz -> mu4 -> QGEO.SYM.01 is the v180/v181 chain (uniformisation, "
"Kerekjarto, order-4 Moebius classification); ledger nodes %s present"
% chain,
have_chain)
# 2. the proposed upstream step is the one new, operator-checkable link
check("PROPOSED UPSTREAM STEP [E-logic]: QGEO.ENERGY.01 (rho^* Lambda_Sigma "
"rho = Lambda_Sigma) => conformality in 2D (Dirichlet-energy invariance "
"is conformal invariance) is the single new link; it is checkable on the "
"DtN operator (Lambda = |k|, the rank-8 Calderon polarisation already in "
"the net construction), unlike the abstract 'is the conformal deck'",
True)
# 3. honest: relocates, does not eliminate
check("RELOCATES, NOT ELIMINATES [O]: 'rho preserves Lambda_Sigma' is "
"plausibly EQUIVALENT to 'rho is the conformal deck' (QGEO.SYM.01) -- in "
"2D, preserving the DtN energy form IS being a conformal symmetry. So "
"QGEO.ENERGY.01 is a sharper, more falsifiable RESTATEMENT of the same "
"bedrock, NOT a theorem, unless rho is defined independently and the "
"invariance independently proven (open). The bedrock stays [O]; same "
"pattern as v179->v181 (each step sharpens but cannot remove the premise)",
"QGEO.SYM.01" in ids)
check("HONEST SCOPE [O]: QGEO.ENERGY.01 is recorded as an upstream/equivalent "
"premise of QGEO.SYM.01, NOT as a closure of GATE.QGEO; it improves "
"checkability (an operator identity on Lambda), not the proof status", True)
return summary("v192 energy-conserving clock: QGEO.ENERGY.01 relocates the bedrock to an operator identity [O]")
if __name__ == "__main__":
raise SystemExit(1 if run() else 0)
Recorded source fingerprint
d9eb0a1fa4811dc540b9ab2513d7a9c9ae4f1d1276c615cf28771230e78e34b0
Paper sections that cite this module
What this source index covers
The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.