Pith Number

pith:PBMB57EO

pith:2015:PBMB57EOWRFAH2MSK57FOPRS7B

not attested not anchored not stored refs pending

Birational splitting and algebraic group actions

Vladimir L. Popov

arxiv:1502.02167 v2 · 2015-02-07 · 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{PBMB57EOWRFAH2MSK57FOPRS7B}

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	2026-05-18T00:28:27.554457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78581efc8eb44a03e992577e573e32f854b6235bd588014c42487cf6b8e60dd2

Aliases

arxiv: 1502.02167 · arxiv_version: 1502.02167v2 · doi: 10.48550/arxiv.1502.02167 · pith_short_12: PBMB57EOWRFA · pith_short_16: PBMB57EOWRFAH2MS · pith_short_8: PBMB57EO

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/PBMB57EOWRFAH2MSK57FOPRS7B \
  | 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: 78581efc8eb44a03e992577e573e32f854b6235bd588014c42487cf6b8e60dd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78ddd7c83fbdc48d0138f8d4d924656b1d35d6fa396faaf8dbb6825e80ff0db4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-02-07T17:39:59Z",
    "title_canon_sha256": "def3ce5a12d97f5ba76ab019f2c42db28c725fee8e9e77a18029ec77b644fae4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.02167",
    "kind": "arxiv",
    "version": 2
  }
}