Pith Number

pith:V47MGXQY

pith:2009:V47MGXQYZUV7ABHJLYQPY35YFS

not attested not anchored not stored refs pending

The type numbers of closed geodesics

I.A. Taimanov

arxiv:0912.5226 v2 · 2009-12-28 · 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{V47MGXQYZUV7ABHJLYQPY35YFS}

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	2026-05-18T02:10:13.413479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af3ec35e18cd2bf004e95e20fc6fb82c996fa2ac70ff898cc142b24f183abd79

Aliases

arxiv: 0912.5226 · arxiv_version: 0912.5226v2 · doi: 10.48550/arxiv.0912.5226 · pith_short_12: V47MGXQYZUV7 · pith_short_16: V47MGXQYZUV7ABHJ · pith_short_8: V47MGXQY

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/V47MGXQYZUV7ABHJLYQPY35YFS \
  | 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: af3ec35e18cd2bf004e95e20fc6fb82c996fa2ac70ff898cc142b24f183abd79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de25d67d22b857286a6322375ebd25dcb615369ee64c649f51cfdf7e53235756",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-12-28T23:37:01Z",
    "title_canon_sha256": "f9f067e1f88a2d32a4791be2bbb362dc029f154f21d1429314a015b8ce57aab7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5226",
    "kind": "arxiv",
    "version": 2
  }
}