Pith Number

pith:4JQX4HIF

pith:2012:4JQX4HIFW7GFALETEM7MLG72TA

not attested not anchored not stored refs pending

Heegaard splittings and singularities of the product map of Morse functions

Kazuto Takao

arxiv:1205.1206 v3 · 2012-05-06 · 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{4JQX4HIFW7GFALETEM7MLG72TA}

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	2026-05-18T03:00:11.566426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2617e1d05b7cc502c93233ec59bfa983c22580a6cd251bb26d347a337e657e3

Aliases

arxiv: 1205.1206 · arxiv_version: 1205.1206v3 · doi: 10.48550/arxiv.1205.1206 · pith_short_12: 4JQX4HIFW7GF · pith_short_16: 4JQX4HIFW7GFALET · pith_short_8: 4JQX4HIF

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/4JQX4HIFW7GFALETEM7MLG72TA \
  | 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: e2617e1d05b7cc502c93233ec59bfa983c22580a6cd251bb26d347a337e657e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2cc1de28f69767221f8055e21628d23097a3828ca7929197d3942acb4b14db3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-05-06T11:31:50Z",
    "title_canon_sha256": "f2094f8b0b5c1b5a6120b1d48e9c1b9e68a0f93418bc4ac4a7f02befe156235d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1206",
    "kind": "arxiv",
    "version": 3
  }
}