Pith Number

pith:NAP2XU3B

pith:2004:NAP2XU3BACBJK3SEBIY3NF27YY

not attested not anchored not stored refs pending

Tannaka Duality for Geometric Stacks

Jacob Lurie

arxiv:math/0412266 v2 · 2004-12-14 · 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{NAP2XU3BACBJK3SEBIY3NF27YY}

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.

Cited by

1 paper in Pith

A Classification of Six Functor Formalisms via Structured Spaces

Receipt and verification

First computed	2026-07-04T14:39:27.676975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

681fabd3610082956e440a31b6975fc61aaea9c8005a7abd9c7fb61d02604034

Aliases

arxiv: math/0412266 · arxiv_version: math/0412266v2 · doi: 10.48550/arxiv.math/0412266 · pith_short_12: NAP2XU3BACBJ · pith_short_16: NAP2XU3BACBJK3SE · pith_short_8: NAP2XU3B

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/NAP2XU3BACBJK3SEBIY3NF27YY \
  | 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: 681fabd3610082956e440a31b6975fc61aaea9c8005a7abd9c7fb61d02604034

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "650648e056a5e8a9b5e56eecda572e1e991c6059fd1e5939955b951f6d7dcdca",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2004-12-14T00:51:56Z",
    "title_canon_sha256": "828a274a32a59f2ebd4ed02c9f4af9ad14e52790376ca69b9f2be09dac440368"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412266",
    "kind": "arxiv",
    "version": 2
  }
}