Pith Number

pith:C5BS4LNS

pith:2011:C5BS4LNSJOFALKIO6TWO6NWJ2L

not attested not anchored not stored refs pending

On stably free modules over affine algebras

Jean Fasel, Ravi A. Rao, Richard G. Swan

arxiv:1107.1051 v2 · 2011-07-06 · 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{C5BS4LNSJOFALKIO6TWO6NWJ2L}

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	2026-05-18T03:44:47.403920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17432e2db24b8a05a90ef4ecef36c9d2d22fef0024f6f5cfaab5379d81a4861a

Aliases

arxiv: 1107.1051 · arxiv_version: 1107.1051v2 · doi: 10.48550/arxiv.1107.1051 · pith_short_12: C5BS4LNSJOFA · pith_short_16: C5BS4LNSJOFALKIO · pith_short_8: C5BS4LNS

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/C5BS4LNSJOFALKIO6TWO6NWJ2L \
  | 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: 17432e2db24b8a05a90ef4ecef36c9d2d22fef0024f6f5cfaab5379d81a4861a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f5566a755cec4444c48b23a3bd8a1bd32ee76f9de6267743c70408facc3b161",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-07-06T08:14:25Z",
    "title_canon_sha256": "36494746ffb1c50f20a19eb94568e8665fcfa469780944b1edc5088568526439"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1051",
    "kind": "arxiv",
    "version": 2
  }
}