Pith Number

pith:BCZXQR3R

pith:2016:BCZXQR3RNPZ6L5HYMJXAL5VP3X

not attested not anchored not stored refs pending

Associated points and integral closure of modules

Antoni Rangachev

arxiv:1611.03910 v3 · 2016-11-11 · math.AG · 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{BCZXQR3RNPZ6L5HYMJXAL5VP3X}

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	2026-05-18T00:16:14.754401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08b37847716bf3e5f4f8626e05f6afdde89bc45d359dfb8ffc38aaf6c9120593

Aliases

arxiv: 1611.03910 · arxiv_version: 1611.03910v3 · doi: 10.48550/arxiv.1611.03910 · pith_short_12: BCZXQR3RNPZ6 · pith_short_16: BCZXQR3RNPZ6L5HY · pith_short_8: BCZXQR3R

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/BCZXQR3RNPZ6L5HYMJXAL5VP3X \
  | 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: 08b37847716bf3e5f4f8626e05f6afdde89bc45d359dfb8ffc38aaf6c9120593

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11642e58b2f6c968730dda71f7796a7d031d08a71b1b7cc2e0f140611587b8d0",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-11-11T23:34:35Z",
    "title_canon_sha256": "f860b0ba3cb85740d3fac3c09a4428a102a91d58e6b24862e2a254da8478c730"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.03910",
    "kind": "arxiv",
    "version": 3
  }
}