Pith Number

pith:NHN5KSVP

pith:2022:NHN5KSVPQLJCDY4Y25IHYLALGM

not attested not anchored not stored refs pending

Torsion and torsion-free classes from objects of finite type in Grothendieck categories

Carlos E. Parra, Daniel Bravo, Marco A. P\'erez, Sinem Odaba\c{s}{\i}

arxiv:2201.02224 v1 · 2022-01-06 · math.CT · 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{NHN5KSVPQLJCDY4Y25IHYLALGM}

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	2026-07-05T04:44:41.818326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69dbd54aaf82d221e398d7507c2c0b33110d0f058eb436ddc0fd951ada657a05

Aliases

arxiv: 2201.02224 · arxiv_version: 2201.02224v1 · doi: 10.48550/arxiv.2201.02224 · pith_short_12: NHN5KSVPQLJC · pith_short_16: NHN5KSVPQLJCDY4Y · pith_short_8: NHN5KSVP

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/NHN5KSVPQLJCDY4Y25IHYLALGM \
  | 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: 69dbd54aaf82d221e398d7507c2c0b33110d0f058eb436ddc0fd951ada657a05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7d20423bc960c11e5b68df9b12946dafb1afb530a0660743f5b42f25faf3a1c",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2022-01-06T19:44:13Z",
    "title_canon_sha256": "da6b5bc193c5ac1f2c4755ebd121645ffe22f1e73dda08bb8bdd229f3e73fe6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.02224",
    "kind": "arxiv",
    "version": 1
  }
}