Pith Number

pith:3OSQ57XE

pith:2011:3OSQ57XEH3EZVPPQN7PBCUBPCA

not attested not anchored not stored refs pending

Indefinite Morse 2-functions; broken fibrations and generalizations

David T. Gay, Robion Kirby

arxiv:1102.0750 v5 · 2011-02-03 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3OSQ57XEH3EZVPPQN7PBCUBPCA}

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	2026-05-18T01:22:29.124942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dba50efee43ec99abdf06fde11502f101b193fd3c63c66efb04236fb98b4a0cd

Aliases

arxiv: 1102.0750 · arxiv_version: 1102.0750v5 · doi: 10.48550/arxiv.1102.0750 · pith_short_12: 3OSQ57XEH3EZ · pith_short_16: 3OSQ57XEH3EZVPPQ · pith_short_8: 3OSQ57XE

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/3OSQ57XEH3EZVPPQN7PBCUBPCA \
  | 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: dba50efee43ec99abdf06fde11502f101b193fd3c63c66efb04236fb98b4a0cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c9a6fa38d2760ad663596be44a600019af6dba6d6b7b18f226b872ea9a4a765",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-02-03T19:02:01Z",
    "title_canon_sha256": "78495e5168bc061e248bc38b7a777de1506bf3ecae4a4ed819d9b476b224ebc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0750",
    "kind": "arxiv",
    "version": 5
  }
}