Pith Number

pith:J5W35P3V

pith:2021:J5W35P3VZAN4PE45S4OSLX2BSI

not attested not anchored not stored refs pending

Categories of modules, comodules and contramodules over representations

Abhishek Banerjee, Mamta Balodi, Samarpita Ray

arxiv:2106.12237 v2 · 2021-06-23 · math.RA · math.AG · math.CT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J5W35P3VZAN4PE45S4OSLX2BSI}

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	2026-07-05T05:41:14.617237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f6dbebf75c81bc7939d971d25df419201f876fac568b39eed4ecbc821836db7

Aliases

arxiv: 2106.12237 · arxiv_version: 2106.12237v2 · doi: 10.48550/arxiv.2106.12237 · pith_short_12: J5W35P3VZAN4 · pith_short_16: J5W35P3VZAN4PE45 · pith_short_8: J5W35P3V

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/J5W35P3VZAN4PE45S4OSLX2BSI \
  | 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: 4f6dbebf75c81bc7939d971d25df419201f876fac568b39eed4ecbc821836db7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f19ad6da701c2c5c5c47d63276eae5d4a4c056f179e9607aeb31d34adf68edd9",
    "cross_cats_sorted": [
      "math.AG",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2021-06-23T08:48:56Z",
    "title_canon_sha256": "feef70c4d8dfc3c70ca4fbd6624525b62d14d0819b0a5d9d2b51123e9bfcb590"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.12237",
    "kind": "arxiv",
    "version": 2
  }
}