Pith Number

pith:W7MA6Y5S

pith:2009:W7MA6Y5S5A55H3JY4DG4ZVV4QT

not attested not anchored not stored refs pending

On the existence of an invariant non-degenerate bilinear form under a linear map

Krishnendu Gongopadhyay, Ravi S. Kulkarni

arxiv:0903.0826 v3 · 2009-03-04 · 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{W7MA6Y5S5A55H3JY4DG4ZVV4QT}

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	2026-05-18T03:16:06.811511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7d80f63b2e83bd3ed38e0cdccd6bc84ce3233f98663c9cf603df2f3e96a4ec6

Aliases

arxiv: 0903.0826 · arxiv_version: 0903.0826v3 · doi: 10.48550/arxiv.0903.0826 · pith_short_12: W7MA6Y5S5A55 · pith_short_16: W7MA6Y5S5A55H3JY · pith_short_8: W7MA6Y5S

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/W7MA6Y5S5A55H3JY4DG4ZVV4QT \
  | 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: b7d80f63b2e83bd3ed38e0cdccd6bc84ce3233f98663c9cf603df2f3e96a4ec6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83ba34612370ed68cb74bcc50962122b6e74095b282d725be4091f6affdb22fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-03-04T17:50:05Z",
    "title_canon_sha256": "5bf4f087f3454723e6eb902ee8b36f0fd1726d4510ba8c6cca63e0cf2ed5e9b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.0826",
    "kind": "arxiv",
    "version": 3
  }
}