Pith Number

pith:P5OGW4ZY

pith:2021:P5OGW4ZYJPNA6FH46C2XPGNBGY

not attested not anchored not stored refs pending

Syzygies, constant rank, and beyond

Bogdan Rai\c{t}\u{a}, Lisa Nicklasson, Marc H\"ark\"onen

arxiv:2112.12663 v2 · 2021-12-23 · math.AP · 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{P5OGW4ZYJPNA6FH46C2XPGNBGY}

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	2026-07-05T07:29:59.911259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f5c6b73384bda0f14fcf0b57799a136084c83b8494b4700dae63de9a4f066d0

Aliases

arxiv: 2112.12663 · arxiv_version: 2112.12663v2 · doi: 10.48550/arxiv.2112.12663 · pith_short_12: P5OGW4ZYJPNA · pith_short_16: P5OGW4ZYJPNA6FH4 · pith_short_8: P5OGW4ZY

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/P5OGW4ZYJPNA6FH46C2XPGNBGY \
  | 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: 7f5c6b73384bda0f14fcf0b57799a136084c83b8494b4700dae63de9a4f066d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bf126b641b8a2d99c0d7fa23d834760a87f3ada805868099b3930552f9651ca",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-12-23T15:57:35Z",
    "title_canon_sha256": "8bb6f4597249552f5ee4065b87979be9fa8e079f66c8575cc85f18cd2a3e9794"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.12663",
    "kind": "arxiv",
    "version": 2
  }
}