Pith Number

pith:GI5PMAPZ

pith:2011:GI5PMAPZNB25O4WRR7WOPOEAT2

not attested not anchored not stored refs pending

Periodic points of birational maps on projective surfaces

Junyi Xie

arxiv:1106.1825 v2 · 2011-06-09 · math.AG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GI5PMAPZNB25O4WRR7WOPOEAT2}

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	2026-05-18T01:28:21.961011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8

Aliases

arxiv: 1106.1825 · arxiv_version: 1106.1825v2 · doi: 10.48550/arxiv.1106.1825 · pith_short_12: GI5PMAPZNB25 · pith_short_16: GI5PMAPZNB25O4WR · pith_short_8: GI5PMAPZ

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/GI5PMAPZNB25O4WRR7WOPOEAT2 \
  | 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: 323af601f96875d772d18fece7b8809eb7709c544e7c8bf5d12ec0e91fed77c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cba1b2390709a358dfe6e73bd57e4a297a75d4cbf715563048d54388d6fe6b8e",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-06-09T14:06:47Z",
    "title_canon_sha256": "d288d297ac538649e88a0036af08b3ef09c3dc14f950369884d50e422b6d9c4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1825",
    "kind": "arxiv",
    "version": 2
  }
}