Pith Number

pith:P5W4D6QN

pith:2007:P5W4D6QN6T3CXM2MUIVY3P7O6C

not attested not anchored not stored refs pending

Modules of covariants in modular invariant theory

Abraham Broer, Jianjun Chuai

arxiv:0709.0703 v3 · 2007-09-05 · 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{P5W4D6QN6T3CXM2MUIVY3P7O6C}

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	2026-05-18T02:58:12.351276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f6dc1fa0df4f62bb34ca22b8dbfeef0941019fcef310f962c80f045f8187ddf

Aliases

arxiv: 0709.0703 · arxiv_version: 0709.0703v3 · doi: 10.48550/arxiv.0709.0703 · pith_short_12: P5W4D6QN6T3C · pith_short_16: P5W4D6QN6T3CXM2M · pith_short_8: P5W4D6QN

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/P5W4D6QN6T3CXM2MUIVY3P7O6C \
  | 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: 7f6dc1fa0df4f62bb34ca22b8dbfeef0941019fcef310f962c80f045f8187ddf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92f8ca50614de01444d9c80f36f244aca03388d1f7f02c262d885fbe961d054a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2007-09-05T16:47:14Z",
    "title_canon_sha256": "e572913a33cf2e091aa74bcfae86c9772eacf7a2b3c1747b280d2cd9ad7d521b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.0703",
    "kind": "arxiv",
    "version": 3
  }
}