Pith Number

pith:ZGAORZYU

pith:1998:ZGAORZYUTCBXFVW2YRMIJTT2EV

not attested not anchored not stored refs pending

3-manifold invariants and periodicity of homology spheres

Joanna Kania-Bartoszynska, Jozef H. Przytycki, Patrick M. Gilmer

arxiv:math/9807011 v3 · 1998-07-02 · math.GT · 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{ZGAORZYUTCBXFVW2YRMIJTT2EV}

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	2026-05-18T02:41:26.522215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c980e8e714988372d6dac45884ce7a2550993ebcc506651bbfbdbf58d5ffc419

Aliases

arxiv: math/9807011 · arxiv_version: math/9807011v3 · doi: 10.48550/arxiv.math/9807011 · pith_short_12: ZGAORZYUTCBX · pith_short_16: ZGAORZYUTCBXFVW2 · pith_short_8: ZGAORZYU

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/ZGAORZYUTCBXFVW2YRMIJTT2EV \
  | 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: c980e8e714988372d6dac45884ce7a2550993ebcc506651bbfbdbf58d5ffc419

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a425d76e3b9e95e72b457aa519c00a7635c01b88e4b06d82bc2018e34b330a4",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-07-02T22:32:50Z",
    "title_canon_sha256": "2d2f8c26c2ab1473ff7c359a0876562eab00466f55276d33614798d50637fd22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9807011",
    "kind": "arxiv",
    "version": 3
  }
}