Pith Number

pith:G62V7C2J

pith:2026:G62V7C2JSWOW3BR6OMMYYFVVHC

not attested not anchored not stored refs pending

Regions represented as foliated forms and natural smooth maps onto them

Naoki Kitazawa

arxiv:2607.17180 v1 · 2026-07-19 · math.AG · math.DG · math.DS · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G62V7C2JSWOW3BR6OMMYYFVVHC}

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

1 paper in Pith

Fundamental examples of height functions on closed manifolds and their 1st derivatives

Receipt and verification

First computed	2026-07-21T01:21:19.563403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37b55f8b49959d6d863e73198c16b5388c4fc6bb813005a3fedc1ee4973de599

Aliases

arxiv: 2607.17180 · arxiv_version: 2607.17180v1 · doi: 10.48550/arxiv.2607.17180 · pith_short_12: G62V7C2JSWOW · pith_short_16: G62V7C2JSWOW3BR6 · pith_short_8: G62V7C2J

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/G62V7C2JSWOW3BR6OMMYYFVVHC \
  | 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: 37b55f8b49959d6d863e73198c16b5388c4fc6bb813005a3fedc1ee4973de599

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7c618b419923f7b92e338b88eb7e292602bcbd1d8830f7b69936d419a876078",
    "cross_cats_sorted": [
      "math.DG",
      "math.DS",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-19T10:35:38Z",
    "title_canon_sha256": "50b483f9b4abfb4bd090655eb703b08c2e8f9adf1b998597b0a7978547bb3a29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17180",
    "kind": "arxiv",
    "version": 1
  }
}