Pith Number

pith:GINUZ6QV

pith:2011:GINUZ6QV75CQMCYCB6BOHFFXBZ

not attested not anchored not stored refs pending

An Algebraic Proof for the Identities for Degree of Syzygies in Numerical Semigroup

Ivan Martino, Neeraj Kumar

arxiv:1109.5331 v1 · 2011-09-25 · 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{GINUZ6QV75CQMCYCB6BOHFFXBZ}

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	2026-05-18T03:53:54.730337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

321b4cfa15ff45060b020f82e394b70e7230ee4d5b45ea52d48695592bfb0bd3

Aliases

arxiv: 1109.5331 · arxiv_version: 1109.5331v1 · doi: 10.48550/arxiv.1109.5331 · pith_short_12: GINUZ6QV75CQ · pith_short_16: GINUZ6QV75CQMCYC · pith_short_8: GINUZ6QV

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/GINUZ6QV75CQMCYCB6BOHFFXBZ \
  | 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: 321b4cfa15ff45060b020f82e394b70e7230ee4d5b45ea52d48695592bfb0bd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbaeda7928d4305a38665c040b965976e34bfc7b101b3cff1c24dd0635b5b8cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-09-25T07:13:16Z",
    "title_canon_sha256": "f942d268ba80c7607cbdf3f94431f50e8b361d094148066445d40ff4ee016c05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5331",
    "kind": "arxiv",
    "version": 1
  }
}