Pith Number

pith:3PHZSDZF

pith:2014:3PHZSDZFEG4HPCGLL6OAYYLTXH

not attested not anchored not stored refs pending

On the limit of Frobenius in the Grothendieck group

Kazuhiko Kurano, Kosuke Ohta

arxiv:1407.4159 v1 · 2014-07-15 · 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{3PHZSDZFEG4HPCGLL6OAYYLTXH}

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	2026-05-18T02:47:30.973763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbcf990f2521b87788cb5f9c0c6173b9d9e06c193cbbe9a834a6aab0fca0f4b7

Aliases

arxiv: 1407.4159 · arxiv_version: 1407.4159v1 · doi: 10.48550/arxiv.1407.4159 · pith_short_12: 3PHZSDZFEG4H · pith_short_16: 3PHZSDZFEG4HPCGL · pith_short_8: 3PHZSDZF

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/3PHZSDZFEG4HPCGLL6OAYYLTXH \
  | 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: dbcf990f2521b87788cb5f9c0c6173b9d9e06c193cbbe9a834a6aab0fca0f4b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7df665c9926b00ccdb16ddaf4b2a34ed5b5dca4a94c6b959b1d8c6ad78b6e1f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2014-07-15T21:56:15Z",
    "title_canon_sha256": "6a77dc73b657f17b1cf84f72e77569bac9220d04d1ea0f841039f3c222219492"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.4159",
    "kind": "arxiv",
    "version": 1
  }
}