Pith Number

pith:GTUAE5SD

pith:2009:GTUAE5SDRJ7JCGMAUOPCFZCVA3

not attested not anchored not stored refs pending

Factorization Rules in Quantum Teichm\"uller Theory

Julien Roger

arxiv:0911.2510 v2 · 2009-11-13 · math.GT · math-ph · math.MP · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTUAE5SDRJ7JCGMAUOPCFZCVA3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Quantized Geodesic Lengths for Teichm\"uller Spaces: Algebraic Aspects

Receipt and verification

First computed	2026-05-18T02:41:51.047945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34e80276438a7e911980a39e22e45506c49961b49bfa55441ab2f82efb3d338f

Aliases

arxiv: 0911.2510 · arxiv_version: 0911.2510v2 · doi: 10.48550/arxiv.0911.2510 · pith_short_12: GTUAE5SDRJ7J · pith_short_16: GTUAE5SDRJ7JCGMA · pith_short_8: GTUAE5SD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GTUAE5SDRJ7JCGMAUOPCFZCVA3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 34e80276438a7e911980a39e22e45506c49961b49bfa55441ab2f82efb3d338f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "961ad68b14e0e6aed29325c70e60d1b693c88ffe054760f2178e5bb631214a12",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-11-13T00:04:49Z",
    "title_canon_sha256": "c8792c5b9d1ddb87f23c1415515077f89bf1df54119ce7fd4a8693452b6f66d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2510",
    "kind": "arxiv",
    "version": 2
  }
}