Pith Number

pith:QV6QCJUE

pith:2026:QV6QCJUEM6PFVEZCM3XCOYN6NG

not attested not anchored not stored refs pending

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

Naoki Kitazawa

arxiv:2608.00556 v1 · 2026-08-01 · math.DG · math.AG · 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{QV6QCJUEM6PFVEZCM3XCOYN6NG}

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.

Receipt and verification

First computed	2026-08-04T00:37:25.992604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

857d012684679e5a932266ee2761be69917f25c8c845f38dbb939c14c5014627

Aliases

arxiv: 2608.00556 · arxiv_version: 2608.00556v1 · doi: 10.48550/arxiv.2608.00556 · pith_short_12: QV6QCJUEM6PF · pith_short_16: QV6QCJUEM6PFVEZC · pith_short_8: QV6QCJUE

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/QV6QCJUEM6PFVEZCM3XCOYN6NG \
  | 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: 857d012684679e5a932266ee2761be69917f25c8c845f38dbb939c14c5014627

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "859902aa5edcd90afbc172801af48394270f6dcdacdd70a7455091eeed8c2de8",
    "cross_cats_sorted": [
      "math.AG",
      "math.DS",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-08-01T09:21:36Z",
    "title_canon_sha256": "fbe1c7137acc253ea4e08df8fdfc2e4f8be0a4e7a7f60478ea7349ee80537744"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.00556",
    "kind": "arxiv",
    "version": 1
  }
}