Pith Number

pith:DX3E6YTY

pith:2011:DX3E6YTYB5FH5SABRFAQJR3LHE

not attested not anchored not stored refs pending

Free Cyclic Submodules and Non-Unimodular Vectors

Joanne L. Hall, Metod Saniga

arxiv:1107.3050 v2 · 2011-07-15 · math.CO · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DX3E6YTYB5FH5SABRFAQJR3LHE}

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	2026-05-18T04:15:38.345067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1df64f62780f4a7ec801894104c76b3900dd1891f176ea1b32817c53ed5b0ff1

Aliases

arxiv: 1107.3050 · arxiv_version: 1107.3050v2 · doi: 10.48550/arxiv.1107.3050 · pith_short_12: DX3E6YTYB5FH · pith_short_16: DX3E6YTYB5FH5SAB · pith_short_8: DX3E6YTY

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/DX3E6YTYB5FH5SABRFAQJR3LHE \
  | 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: 1df64f62780f4a7ec801894104c76b3900dd1891f176ea1b32817c53ed5b0ff1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccc2a0429dc5496f659ef0ed28cd497cb16375eaf27ad69a07f2ab6c2a86a2db",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-15T11:56:15Z",
    "title_canon_sha256": "ad1cce1858f164ac3c06984bb240b4f4088a0175530c1c2c876720f563b05ca0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3050",
    "kind": "arxiv",
    "version": 2
  }
}