Pith Number

pith:EKX7NWIL

pith:2013:EKX7NWIL7DIXUXBT5NLE7FJ2D7

not attested not anchored not stored refs pending

Bounds on depth of tensor products of modules

Arash Sadeghi, Olgur Celikbas, Ryo Takahashi

arxiv:1309.7104 v3 · 2013-09-27 · 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{EKX7NWIL7DIXUXBT5NLE7FJ2D7}

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	2026-05-18T00:07:51.397408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22aff6d90bf8d17a5c33eb564f953a1fefe858a078d1d29c5a6b6ae7029dfcf7

Aliases

arxiv: 1309.7104 · arxiv_version: 1309.7104v3 · doi: 10.48550/arxiv.1309.7104 · pith_short_12: EKX7NWIL7DIX · pith_short_16: EKX7NWIL7DIXUXBT · pith_short_8: EKX7NWIL

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/EKX7NWIL7DIXUXBT5NLE7FJ2D7 \
  | 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: 22aff6d90bf8d17a5c33eb564f953a1fefe858a078d1d29c5a6b6ae7029dfcf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f57d1289fde84ff7553aade4bf9dbc6b259328ab900bc1066a94c0780c908ad6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-09-27T02:55:15Z",
    "title_canon_sha256": "796abf1cd60f7e7308ba31cad593d59c823671a81bd15330f3fd4e189f83fd34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7104",
    "kind": "arxiv",
    "version": 3
  }
}