Pith Number

pith:QJNIDXN4

pith:2011:QJNIDXN4U5ZQUA7OH7YMUN3OG5

not attested not anchored not stored refs pending

Special points and Poincar\'e bi-extensions, with an Appendix by Bas Edixhoven

Daniel Bertrand

arxiv:1104.5178 v1 · 2011-04-27 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJNIDXN4U5ZQUA7OH7YMUN3OG5}

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.

Cited by

1 paper in Pith

Unlikely intersections in Shimura varieties and beyond: a survey

Receipt and verification

First computed	2026-05-18T04:23:22.479281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

825a81ddbca7730a03ee3ff0ca376e3777597f1787f7356854566a857f7170e1

Aliases

arxiv: 1104.5178 · arxiv_version: 1104.5178v1 · doi: 10.48550/arxiv.1104.5178 · pith_short_12: QJNIDXN4U5ZQ · pith_short_16: QJNIDXN4U5ZQUA7O · pith_short_8: QJNIDXN4

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/QJNIDXN4U5ZQUA7OH7YMUN3OG5 \
  | 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: 825a81ddbca7730a03ee3ff0ca376e3777597f1787f7356854566a857f7170e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96d9caa1ff4a957843edb1583ad1a91014f0480c2b8ded2373d11032f35e3e64",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-27T16:17:25Z",
    "title_canon_sha256": "584603b194a64e549aa4fc22a94e9edfc6dc77fe2b504dcff4b13628f485ddb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5178",
    "kind": "arxiv",
    "version": 1
  }
}