Pith Number

pith:2RCPLEAR

pith:2007:2RCPLEARY2R4VIZOAYHFZPYXZL

not attested not anchored not stored refs pending

Index reduction for Brauer classes via stable sheaves (with an appendix by Bhargav Bhatt)

Daniel Krashen, Max Lieblich

arxiv:0706.1072 v3 · 2007-06-07 · 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{2RCPLEARY2R4VIZOAYHFZPYXZL}

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	2026-05-18T00:13:14.391508Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d444f59011c6a3caa32e060e5cbf17cae5bd4e3d0fddce5d8ba9812e55ed5fec

Aliases

arxiv: 0706.1072 · arxiv_version: 0706.1072v3 · doi: 10.48550/arxiv.0706.1072 · pith_short_12: 2RCPLEARY2R4 · pith_short_16: 2RCPLEARY2R4VIZO · pith_short_8: 2RCPLEAR

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/2RCPLEARY2R4VIZOAYHFZPYXZL \
  | 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: d444f59011c6a3caa32e060e5cbf17cae5bd4e3d0fddce5d8ba9812e55ed5fec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd557f17aaefd371cb49389b27f2edc87d698f89c6376e2aecd0ff3fcddb457e",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-06-07T20:13:57Z",
    "title_canon_sha256": "fad450e19dd03ad098fa4b32c03764316b921dfe01295ade8a6bcb6e88501e66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.1072",
    "kind": "arxiv",
    "version": 3
  }
}