Pith Number

pith:WZVO2D2F

pith:2015:WZVO2D2FH55NNJFNWTDS3CRGQQ

not attested not anchored not stored refs pending

Directed Unions of Local Quadratic Transforms of a Regular Local Ring

Matthew Toeniskoetter, Mee-Kyoung Kim, William Heinzer

arxiv:1512.03848 v2 · 2015-12-11 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WZVO2D2FH55NNJFNWTDS3CRGQQ}

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	2026-05-18T01:23:28.615959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b66aed0f453f7ad6a4adb4c72d8a2684111c13ab25ee08e0a50e39dfcfde6234

Aliases

arxiv: 1512.03848 · arxiv_version: 1512.03848v2 · doi: 10.48550/arxiv.1512.03848 · pith_short_12: WZVO2D2FH55N · pith_short_16: WZVO2D2FH55NNJFN · pith_short_8: WZVO2D2F

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/WZVO2D2FH55NNJFNWTDS3CRGQQ \
  | 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: b66aed0f453f7ad6a4adb4c72d8a2684111c13ab25ee08e0a50e39dfcfde6234

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "167a8932e715cfbb3ace6814edda567d57428d47cd302bc8094216187d543fe0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-12-11T23:26:04Z",
    "title_canon_sha256": "1b687b1f4671a79fe05cd9999cb2884ec2fa1323463adbb46e59e2a9a456263f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03848",
    "kind": "arxiv",
    "version": 2
  }
}