Pith Number

pith:RQSU2QBW

pith:2015:RQSU2QBWH2UITG5YVSN4WQH7HR

not attested not anchored not stored refs pending

Compact affine manifolds with precompact holonomy are geodesically complete

Luis Ak\'e Hau, Miguel S\'anchez

arxiv:1511.03605 v2 · 2015-11-11 · math.DG · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RQSU2QBWH2UITG5YVSN4WQH7HR}

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	2026-05-18T01:24:02.994341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c254d40363ea8899bb8ac9bcb40ff3c4b467a5bcebc44cc29e51bcc3203ff94

Aliases

arxiv: 1511.03605 · arxiv_version: 1511.03605v2 · doi: 10.48550/arxiv.1511.03605 · pith_short_12: RQSU2QBWH2UI · pith_short_16: RQSU2QBWH2UITG5Y · pith_short_8: RQSU2QBW

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/RQSU2QBWH2UITG5YVSN4WQH7HR \
  | 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: 8c254d40363ea8899bb8ac9bcb40ff3c4b467a5bcebc44cc29e51bcc3203ff94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81e022973141d4c48214f00eef54d1952d7dce18dda817f57564c6ab0a691057",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-11-11T19:06:36Z",
    "title_canon_sha256": "7bba6b9177d0dd1568c58be84e94117d95fca37a144483d0289e6b91398eb2aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03605",
    "kind": "arxiv",
    "version": 2
  }
}