Pith Number

pith:BZIPD3CA

pith:2016:BZIPD3CAOST7Y236VRSHKTPOFN

not attested not anchored not stored refs pending

Grothendieck duality and Q-Gorenstein morphisms

Noboru Nakayama, Yongnam Lee

arxiv:1612.01690 v1 · 2016-12-06 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BZIPD3CAOST7Y236VRSHKTPOFN}

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	2026-05-18T00:55:47.827736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e50f1ec4074a7fc6b7eac64754dee2b768f78edd4215ca1edf3767102f27a62

Aliases

arxiv: 1612.01690 · arxiv_version: 1612.01690v1 · doi: 10.48550/arxiv.1612.01690 · pith_short_12: BZIPD3CAOST7 · pith_short_16: BZIPD3CAOST7Y236 · pith_short_8: BZIPD3CA

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/BZIPD3CAOST7Y236VRSHKTPOFN \
  | 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: 0e50f1ec4074a7fc6b7eac64754dee2b768f78edd4215ca1edf3767102f27a62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9012edd60998e41ef4740227eb4dd51e54a04e5c27320dcf0b69c5334f9a32be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-12-06T07:44:40Z",
    "title_canon_sha256": "43a75a52820e87db6c8a9fbe58fd363b3a982cb6e3cce4cc47192a242243462c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01690",
    "kind": "arxiv",
    "version": 1
  }
}