Pith Number

pith:THGRBPVQ

pith:2002:THGRBPVQCYJN4OXVPGH42EYGV5

not attested not anchored not stored refs pending

Casson invariant of knots associated with divides

Alexander Shumakovitch

arxiv:math/0209412 v1 · 2002-09-30 · 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{THGRBPVQCYJN4OXVPGH42EYGV5}

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	2026-07-04T14:36:29.721989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99cd10beb01612de3af5798fcd1306af738343a1f93fdb7fe626521141bc81b6

Aliases

arxiv: math/0209412 · arxiv_version: math/0209412v1 · doi: 10.48550/arxiv.math/0209412 · pith_short_12: THGRBPVQCYJN · pith_short_16: THGRBPVQCYJN4OXV · pith_short_8: THGRBPVQ

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/THGRBPVQCYJN4OXVPGH42EYGV5 \
  | 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: 99cd10beb01612de3af5798fcd1306af738343a1f93fdb7fe626521141bc81b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb8f16065c6e4ce6f6338be10e4d7bcfd755a077b68ab6f52276a7a110435b4a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-09-30T19:18:28Z",
    "title_canon_sha256": "f5c867c485d5f12a4607fa80206642fd4905a49547080a5dbc5a95cdf373b8a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209412",
    "kind": "arxiv",
    "version": 1
  }
}