Pith Number

pith:HXFMJTYR

pith:2018:HXFMJTYRH7JDMH6JFTSSMWENRO

not attested not anchored not stored refs pending

Realization of a graph as the Reeb graph of a Morse function on a manifold

{\L}ukasz Patryk Michalak

arxiv:1805.06727 v2 · 2018-05-17 · 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{HXFMJTYRH7JDMH6JFTSSMWENRO}

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.

Cited by

2 papers in Pith

Representations of Reeb spaces via simplified graphs and examples

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles

Receipt and verification

First computed	2026-05-17T23:56:20.763491Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dcac4cf113fd2361fc92ce526588d8b83752067b45c8e9edad5a60ec4b49319

Aliases

arxiv: 1805.06727 · arxiv_version: 1805.06727v2 · doi: 10.48550/arxiv.1805.06727 · pith_short_12: HXFMJTYRH7JD · pith_short_16: HXFMJTYRH7JDMH6J · pith_short_8: HXFMJTYR

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/HXFMJTYRH7JDMH6JFTSSMWENRO \
  | 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: 3dcac4cf113fd2361fc92ce526588d8b83752067b45c8e9edad5a60ec4b49319

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "406822390a0660cba8facbf67c80be282cc4870fd5b8252b3bab8f30dbda9440",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-05-17T12:36:45Z",
    "title_canon_sha256": "986badb2b10f4876ca71a11a30da63746b9e1c8578bae192616596bc6c2a39ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.06727",
    "kind": "arxiv",
    "version": 2
  }
}