Pith Number

pith:VR6FZQVE

pith:2010:VR6FZQVEXSNXJGUZ6OKYZN27S4

not attested not anchored not stored refs pending

The Frobenius vector of a free affine semigroup

Abdallah Assi

arxiv:1012.1442 v2 · 2010-12-07 · math.NT · 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{VR6FZQVEXSNXJGUZ6OKYZN27S4}

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	2026-05-18T04:10:58.748679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac7c5cc2a4bc9b749a99f3958cb75f972f6d33fa49e4148224618fcfaaa70682

Aliases

arxiv: 1012.1442 · arxiv_version: 1012.1442v2 · doi: 10.48550/arxiv.1012.1442 · pith_short_12: VR6FZQVEXSNX · pith_short_16: VR6FZQVEXSNXJGUZ · pith_short_8: VR6FZQVE

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/VR6FZQVEXSNXJGUZ6OKYZN27S4 \
  | 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: ac7c5cc2a4bc9b749a99f3958cb75f972f6d33fa49e4148224618fcfaaa70682

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "600b380aad2a794ceba09fa8feaad1a186bb329ff6cc3c245729a1bc8dd4f287",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-07T10:01:53Z",
    "title_canon_sha256": "39eeed2d27f436c2478567f175e0e3050dff4308fde6923f14829bb7fb5b4a83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1442",
    "kind": "arxiv",
    "version": 2
  }
}