Pith Number

pith:KDUZ7YY2

pith:2016:KDUZ7YY2OJ3MSTFRU2OJZZL6IN

not attested not anchored not stored refs pending

The closure constraint for the hyperbolic tetrahedron as a Bianchi identity

Christoph Charles, Etera R. Livine

arxiv:1607.08359 v1 · 2016-07-28 · gr-qc · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KDUZ7YY2OJ3MSTFRU2OJZZL6IN}

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	2026-05-18T00:41:26.070324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50e99fe31a7276c94cb1a69c9ce57e43479b2141e7cf1b58930fdaf992e0c8fe

Aliases

arxiv: 1607.08359 · arxiv_version: 1607.08359v1 · doi: 10.48550/arxiv.1607.08359 · pith_short_12: KDUZ7YY2OJ3M · pith_short_16: KDUZ7YY2OJ3MSTFR · pith_short_8: KDUZ7YY2

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/KDUZ7YY2OJ3MSTFRU2OJZZL6IN \
  | 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: 50e99fe31a7276c94cb1a69c9ce57e43479b2141e7cf1b58930fdaf992e0c8fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00fbca0959b12218c9bd55ea2c53e07822617151f650711ba71058f8b3802094",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-07-28T08:48:39Z",
    "title_canon_sha256": "118042d7077d79ab39a43aa4dff89080bb8b804c4021dfbb3de699430d11d180"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.08359",
    "kind": "arxiv",
    "version": 1
  }
}