Pith Number

pith:KZNRVN3Z

pith:2025:KZNRVN3Z7KTFCX427V6US43TSZ

not attested not anchored not stored refs pending

The equations of Gauss, Codazzi and Ricci of surfaces in 4-dimensional space forms

Naoya Ando

arxiv:2505.13874 v3 · 2025-05-20 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KZNRVN3Z7KTFCX427V6US43TSZ}

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	2026-06-08T01:03:44.862619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

565b1ab779faa6515f9afd7d497373966fdbf249d7b3ae067b9d8f031785cb17

Aliases

arxiv: 2505.13874 · arxiv_version: 2505.13874v3 · doi: 10.48550/arxiv.2505.13874 · pith_short_12: KZNRVN3Z7KTF · pith_short_16: KZNRVN3Z7KTFCX42 · pith_short_8: KZNRVN3Z

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/KZNRVN3Z7KTFCX427V6US43TSZ \
  | 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: 565b1ab779faa6515f9afd7d497373966fdbf249d7b3ae067b9d8f031785cb17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04f9393a1c68d06fd2b2a497f1a87a63ad74935af8368c32d9874caf5179ee8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-05-20T03:29:49Z",
    "title_canon_sha256": "40ddd5c854784190be6c523f048e8651633fcec5a93311ecef7047a58b892d2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.13874",
    "kind": "arxiv",
    "version": 3
  }
}