Pith Number

pith:VXZZA6FE

pith:2013:VXZZA6FEOK6GVNFFVUVTF2VCOH

not attested not anchored not stored refs pending

Homotopy theory of modules over diagrams of rings

B. Shipley, J. P. C. Greenlees

arxiv:1309.6997 v1 · 2013-09-26 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXZZA6FEOK6GVNFFVUVTF2VCOH}

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	2026-05-18T03:12:09.545078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adf39078a472bc6ab4a5ad2b32eaa271daf86979ce82268e40d96505695eda63

Aliases

arxiv: 1309.6997 · arxiv_version: 1309.6997v1 · doi: 10.48550/arxiv.1309.6997 · pith_short_12: VXZZA6FEOK6G · pith_short_16: VXZZA6FEOK6GVNFF · pith_short_8: VXZZA6FE

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/VXZZA6FEOK6GVNFFVUVTF2VCOH \
  | 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: adf39078a472bc6ab4a5ad2b32eaa271daf86979ce82268e40d96505695eda63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8f9889199623b522a3b7adef7d384ae8400731a12d7e5e5f7a9ea4df3b97806",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2013-09-26T18:17:34Z",
    "title_canon_sha256": "ab6ae3c70a64addc9ad91a2ffea20ca3d37b21c49d75561a5a807b67d6506838"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6997",
    "kind": "arxiv",
    "version": 1
  }
}