Pith Number

pith:2VNFEVB7

pith:2015:2VNFEVB7IIIQOUDS5VHFPSYMJJ

not attested not anchored not stored refs pending

Independence of $\ell$ for the supports in the Decomposition Theorem

Shenghao Sun

arxiv:1512.01447 v2 · 2015-12-04 · 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{2VNFEVB7IIIQOUDS5VHFPSYMJJ}

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	2026-05-18T00:08:05.442515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333

Aliases

arxiv: 1512.01447 · arxiv_version: 1512.01447v2 · doi: 10.48550/arxiv.1512.01447 · pith_short_12: 2VNFEVB7IIIQ · pith_short_16: 2VNFEVB7IIIQOUDS · pith_short_8: 2VNFEVB7

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/2VNFEVB7IIIQOUDS5VHFPSYMJJ \
  | 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: d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4225c081b77de39316847990ded2be00d10f97a9eb5192d6c2f837fd9466041",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-12-04T15:16:47Z",
    "title_canon_sha256": "15c74a98a5e8f7bfacd6b4531f2a177860580fd0c2f2c2c0b8d709c5ddab13ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01447",
    "kind": "arxiv",
    "version": 2
  }
}