Pith Number

pith:5RGSM3G4

pith:2004:5RGSM3G4KKBVT3OSVE5HNM4FAM

not attested not anchored not stored refs pending

End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds

Robert Myers

arxiv:math/0407172 v3 · 2004-07-12 · 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{5RGSM3G4KKBVT3OSVE5HNM4FAM}

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	2026-05-18T02:38:00.031258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec4d266cdc528359edd2a93a76b3850307bc8b916748fc59802734dee0b270f0

Aliases

arxiv: math/0407172 · arxiv_version: math/0407172v3 · doi: 10.48550/arxiv.math/0407172 · pith_short_12: 5RGSM3G4KKBV · pith_short_16: 5RGSM3G4KKBVT3OS · pith_short_8: 5RGSM3G4

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/5RGSM3G4KKBVT3OSVE5HNM4FAM \
  | 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: ec4d266cdc528359edd2a93a76b3850307bc8b916748fc59802734dee0b270f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3eac335938235d168ea6277b9e2a2ce576d9c30b17d81008a5be71f1925bac01",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-07-12T18:28:30Z",
    "title_canon_sha256": "b9b0435e388acb7a30042d99ba2c9d5b5270090cce447e52ca9498c845b35492"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407172",
    "kind": "arxiv",
    "version": 3
  }
}