Pith Number

pith:STRYBG3X

pith:2010:STRYBG3XCNXPH3MSXCXYDK2J2A

not attested not anchored not stored refs pending

An example of Melkersson subcategory which is not closed under injective hulls

Takeshi Yoshizawa

arxiv:1011.1663 v2 · 2010-11-07 · 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{STRYBG3XCNXPH3MSXCXYDK2J2A}

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	2026-05-18T04:36:48.959480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94e3809b77136ef3ed92b8af81ab49d014112752a6447e83cca790f1e98cbc33

Aliases

arxiv: 1011.1663 · arxiv_version: 1011.1663v2 · doi: 10.48550/arxiv.1011.1663 · pith_short_12: STRYBG3XCNXP · pith_short_16: STRYBG3XCNXPH3MS · pith_short_8: STRYBG3X

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/STRYBG3XCNXPH3MSXCXYDK2J2A \
  | 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: 94e3809b77136ef3ed92b8af81ab49d014112752a6447e83cca790f1e98cbc33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d5af3e9c85dff07d0ebe9292ebf8a716f598ed1bf4259b8d5acfa875b946acd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-11-07T17:52:23Z",
    "title_canon_sha256": "4a6d420c50b922cf24d795f1a743e8596d3da13551279b84958fca1ee0de2a50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1663",
    "kind": "arxiv",
    "version": 2
  }
}