Pith Number

pith:XMVICSFW

pith:2011:XMVICSFWJCSW7Q7GELFIPZGJ6C

not attested not anchored not stored refs pending

Elliptic fibrations on the modular surface associated to \Gamma_1(8)

Marie Jos\'e Bertin, Odile Lecacheux

arxiv:1105.6312 v1 · 2011-05-31 · math.AG · 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{XMVICSFWJCSW7Q7GELFIPZGJ6C}

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	2026-05-18T04:19:42.890117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb2a8148b648a56fc3e622ca87e4c9f09f9fa7b0c507c2fb85d630f1aa072feb

Aliases

arxiv: 1105.6312 · arxiv_version: 1105.6312v1 · doi: 10.48550/arxiv.1105.6312 · pith_short_12: XMVICSFWJCSW · pith_short_16: XMVICSFWJCSW7Q7G · pith_short_8: XMVICSFW

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/XMVICSFWJCSW7Q7GELFIPZGJ6C \
  | 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: bb2a8148b648a56fc3e622ca87e4c9f09f9fa7b0c507c2fb85d630f1aa072feb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e61e902323e5e47d236d8ebaf912659612003fcb5350bc707bc75d9827c9baa9",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-05-31T15:15:55Z",
    "title_canon_sha256": "61cee6f08be2ba10e47492ccfe0bc61160325e8c5314f4bbe21f618198924142"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.6312",
    "kind": "arxiv",
    "version": 1
  }
}