Pith Number

pith:UEXI6G6M

pith:2019:UEXI6G6M4VBYMWOABWWQG5I6D5

not attested not anchored not stored refs pending

On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Naoki Kitazawa

arxiv:1902.08841 v5 · 2019-02-23 · 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{UEXI6G6M4VBYMWOABWWQG5I6D5}

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

3 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	2026-07-05T03:00:43.833372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99

Aliases

arxiv: 1902.08841 · arxiv_version: 1902.08841v5 · doi: 10.48550/arxiv.1902.08841 · pith_short_12: UEXI6G6M4VBY · pith_short_16: UEXI6G6M4VBYMWOA · pith_short_8: UEXI6G6M

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/UEXI6G6M4VBYMWOABWWQG5I6D5 \
  | 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: a12e8f1bcce5438659c00dad03751e1f5093210ea1af0add0b057449632cca99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88ca4e50e035c92469066cc0bf7a5b3a9a72df182c33330184c6d50d145f021c",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-02-23T19:55:38Z",
    "title_canon_sha256": "5b57ee4b1af60a17ca6001243f489b1f9798c9b76a1936c65564e4cb95d9d386"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.08841",
    "kind": "arxiv",
    "version": 5
  }
}