Pith Number

pith:7ZJKIWBE

pith:2011:7ZJKIWBEO62SJM2EVZXOCG3CAQ

not attested not anchored not stored refs pending

On the fields generated by the lengths of closed geodesics in locally symmetric spaces

Andrei S. Rapinchuk, Gopal Prasad

arxiv:1110.0141 v1 · 2011-10-02 · math.DG · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZJKIWBEO62SJM2EVZXOCG3CAQ}

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	2026-05-18T04:11:50.692933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe52a4582477b524b344ae6ee11b62042f81f81502331d00de93634683de4d69

Aliases

arxiv: 1110.0141 · arxiv_version: 1110.0141v1 · doi: 10.48550/arxiv.1110.0141 · pith_short_12: 7ZJKIWBEO62S · pith_short_16: 7ZJKIWBEO62SJM2E · pith_short_8: 7ZJKIWBE

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/7ZJKIWBEO62SJM2EVZXOCG3CAQ \
  | 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: fe52a4582477b524b344ae6ee11b62042f81f81502331d00de93634683de4d69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecd0c8a54e5bf5e5c4fa0a246d7daf5af878adb4c76d31dff1156ecabd3de9d2",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-10-02T00:02:28Z",
    "title_canon_sha256": "8b8f144461b00edc5f4f7d5cfc14abd5204b37777812c1571a947423b80d76cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.0141",
    "kind": "arxiv",
    "version": 1
  }
}