Pith Number

pith:MM7BHI4O

pith:2019:MM7BHI4O6ECDXQU55R3W3NREEC

not attested not anchored not stored refs pending

On Reeb graphs induced from smooth functions on closed or open manifolds

Naoki Kitazawa

arxiv:1908.04340 v8 · 2019-08-12 · math.GT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MM7BHI4O6ECDXQU55R3W3NREEC}

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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

Receipt and verification

First computed	2026-07-05T04:08:22.826863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

633e13a38ef1043bc29dec776db6242087437ca876102831cdec167f8e5422dc

Aliases

arxiv: 1908.04340 · arxiv_version: 1908.04340v8 · doi: 10.48550/arxiv.1908.04340 · pith_short_12: MM7BHI4O6ECD · pith_short_16: MM7BHI4O6ECDXQU5 · pith_short_8: MM7BHI4O

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/MM7BHI4O6ECDXQU55R3W3NREEC \
  | 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: 633e13a38ef1043bc29dec776db6242087437ca876102831cdec167f8e5422dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9226665ae445784d594b55163270d0cf1b3f22692bda87917cf3c3ba3ec562a2",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-08-12T19:11:23Z",
    "title_canon_sha256": "e970fb7e3979a9b765e5ba88693be1875066f9d1e4d95aead0e283d4e77ffb70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.04340",
    "kind": "arxiv",
    "version": 8
  }
}