Pith Number

pith:7W2DVLEG

pith:2019:7W2DVLEGAJBZ6KD3BORVQMS7NU

not attested not anchored not stored refs pending

Maps on manifolds onto graphs locally regarded as the quotient maps onto Reeb spaces of some differentiable maps and a new construction problem

Naoki Kitazawa

arxiv:1909.10315 v4 · 2019-09-16 · math.GT · math.GN

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7W2DVLEGAJBZ6KD3BORVQMS7NU}

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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	2026-07-05T04:00:10.643416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdb43aac8602439f287b0ba358325f6d2fb8287edd3666ea0a3953b5e669accf

Aliases

arxiv: 1909.10315 · arxiv_version: 1909.10315v4 · doi: 10.48550/arxiv.1909.10315 · pith_short_12: 7W2DVLEGAJBZ · pith_short_16: 7W2DVLEGAJBZ6KD3 · pith_short_8: 7W2DVLEG

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/7W2DVLEGAJBZ6KD3BORVQMS7NU \
  | 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: fdb43aac8602439f287b0ba358325f6d2fb8287edd3666ea0a3953b5e669accf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2ccf2e3d9095bdaa52b4f27dc34712c27c6c7d985b8c6fc12afe0d552789f28",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-09-16T23:18:57Z",
    "title_canon_sha256": "e19698aed3e049bd96bc4f09f19f04d8f0df2bebc690eeff2dfe559374fda009"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.10315",
    "kind": "arxiv",
    "version": 4
  }
}