Pith Number

pith:FNOJGSXI

pith:2016:FNOJGSXIJRZZFH5PI5KKSXFOG6

not attested not anchored not stored refs pending

Phantom covering ideals in categories without enough projective morphisms

Pedro A. Guil Asensio, Sergio Estrada, Sinem Odabasi

arxiv:1607.06529 v2 · 2016-07-21 · math.KT · 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{FNOJGSXIJRZZFH5PI5KKSXFOG6}

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	2026-05-17T23:44:43.656745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b5c934ae84c73929faf4754a95cae37a010a9ed3de1c04ae31839e595761017

Aliases

arxiv: 1607.06529 · arxiv_version: 1607.06529v2 · doi: 10.48550/arxiv.1607.06529 · pith_short_12: FNOJGSXIJRZZ · pith_short_16: FNOJGSXIJRZZFH5P · pith_short_8: FNOJGSXI

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/FNOJGSXIJRZZFH5PI5KKSXFOG6 \
  | 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: 2b5c934ae84c73929faf4754a95cae37a010a9ed3de1c04ae31839e595761017

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83cad760da4531aa007bca615b3728f7fe2ee1355f7431dc8e7bc9dc7e00acdf",
    "cross_cats_sorted": [
      "math.AG",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2016-07-21T23:35:42Z",
    "title_canon_sha256": "6b1a0190c2d280926ea7fa88a072bd367d0d5f359374147e55b1af6540c9bf44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.06529",
    "kind": "arxiv",
    "version": 2
  }
}