Pith Number

pith:VPVVIBXF

pith:2011:VPVVIBXF4I2Q2VGJLFT4CAL55Q

not attested not anchored not stored refs pending

Rank two globally generated vector bundles with c_1 \leq 5

Ludovica Chiodera, Philippe Ellia

arxiv:1111.5725 v1 · 2011-11-24 · 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{VPVVIBXF4I2Q2VGJLFT4CAL55Q}

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	2026-05-18T04:07:42.481282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abeb5406e5e2350d54c95967c1017dec3fbce87e0bcfd58c95d710d59ded7ffd

Aliases

arxiv: 1111.5725 · arxiv_version: 1111.5725v1 · doi: 10.48550/arxiv.1111.5725 · pith_short_12: VPVVIBXF4I2Q · pith_short_16: VPVVIBXF4I2Q2VGJ · pith_short_8: VPVVIBXF

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/VPVVIBXF4I2Q2VGJLFT4CAL55Q \
  | 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: abeb5406e5e2350d54c95967c1017dec3fbce87e0bcfd58c95d710d59ded7ffd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "583ef0bb05dd53f1d13c9007427129519b76c0b52e1cc2e9aab94d6ac51798cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-11-24T11:18:30Z",
    "title_canon_sha256": "5a0238d4b0ee2ea11af676662cb2826c569fb78279d59e63782eebac28f87c72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5725",
    "kind": "arxiv",
    "version": 1
  }
}