Pith Number

pith:T6V22XKO

pith:2013:T6V22XKOUBRGCGJQ32EY63BCG6

not attested not anchored not stored refs pending

Some duality and equivalence results

Majid Rahro Zargar

arxiv:1308.3071 v2 · 2013-08-14 · 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{T6V22XKOUBRGCGJQ32EY63BCG6}

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	2026-05-18T01:34:51.255391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fabad5d4ea062611930de898f6c22379fa6cb094cb131e1360e366083f1ed78

Aliases

arxiv: 1308.3071 · arxiv_version: 1308.3071v2 · doi: 10.48550/arxiv.1308.3071 · pith_short_12: T6V22XKOUBRG · pith_short_16: T6V22XKOUBRGCGJQ · pith_short_8: T6V22XKO

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/T6V22XKOUBRGCGJQ32EY63BCG6 \
  | 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: 9fabad5d4ea062611930de898f6c22379fa6cb094cb131e1360e366083f1ed78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "911f9b61686ba1beb4ea6ff641ffa14a4474a7b8d40c0eaa9f40baf2a88c81fc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-08-14T09:34:03Z",
    "title_canon_sha256": "579298f55d063a64e2bede7324d3de5b2ee9673057840ce912635876312fffc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3071",
    "kind": "arxiv",
    "version": 2
  }
}