Pith Number

pith:E2IQUILZ

pith:2003:E2IQUILZLU7JGELB3GBWCNYSOL

not attested not anchored not stored refs pending

Reidemeister-Turaev torsion modulo one of rational homology three-spheres

Florian Deloup, Gwenael Massuyeau

arxiv:math/0301041 v3 · 2003-01-06 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E2IQUILZLU7JGELB3GBWCNYSOL}

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.

Receipt and verification

First computed	2026-05-18T02:38:00.471193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26910a21795d3e931161d98361371272d3fafde07bb0ccb1aefbead8e1e18b24

Aliases

arxiv: math/0301041 · arxiv_version: math/0301041v3 · doi: 10.48550/arxiv.math/0301041 · pith_short_12: E2IQUILZLU7J · pith_short_16: E2IQUILZLU7JGELB · pith_short_8: E2IQUILZ

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/E2IQUILZLU7JGELB3GBWCNYSOL \
  | 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: 26910a21795d3e931161d98361371272d3fafde07bb0ccb1aefbead8e1e18b24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a88bd685544633d1849dc71b788d38a5e44e48b4eb64ce1147ef6b4b968f8e8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2003-01-06T15:06:35Z",
    "title_canon_sha256": "80ff24e80461428721f8f77e7429963669b30d37c79bb37ffb1e6b01835845a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0301041",
    "kind": "arxiv",
    "version": 3
  }
}