Pith Number

pith:VEGPQKMM

pith:2025:VEGPQKMMAB44SKO6HCQXFCRZYI

not attested not anchored not stored refs pending

Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity

Leonid Positselski

arxiv:2509.07645 v3 · 2025-09-09 · math.CT · math.AG · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VEGPQKMMAB44SKO6HCQXFCRZYI}

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	2026-07-08T01:19:06.451194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a90cf8298c0079c929de38a1728a39c202d837bb3edcc79fc6f24de916f7db84

Aliases

arxiv: 2509.07645 · arxiv_version: 2509.07645v3 · doi: 10.48550/arxiv.2509.07645 · pith_short_12: VEGPQKMMAB44 · pith_short_16: VEGPQKMMAB44SKO6 · pith_short_8: VEGPQKMM

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/VEGPQKMMAB44SKO6HCQXFCRZYI \
  | 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: a90cf8298c0079c929de38a1728a39c202d837bb3edcc79fc6f24de916f7db84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a0a38f3ef251264306bda0d45d5ec6ab71b1610c00ccb9c5191f499f2d57471",
    "cross_cats_sorted": [
      "math.AG",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-09-09T12:12:42Z",
    "title_canon_sha256": "6f6d34fd1e03f3c01df521653d79a28bd21e3a902d0079a03278f34eca6bbdf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.07645",
    "kind": "arxiv",
    "version": 3
  }
}