Pith Number

pith:DWG3W47O

pith:2007:DWG3W47OS6XA2QG3BGQCAPIVWL

not attested not anchored not stored refs pending

The refined transfer, bundle structures and algebraic K-theory

Bruce Williams, John R. Klein

arxiv:0707.0250 v4 · 2007-07-02 · math.AT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DWG3W47OS6XA2QG3BGQCAPIVWL}

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	2026-05-18T02:58:12.612191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d8dbb73ee97ae0d40db09a0203d15b2fffb6640a549e2dcad705de79225f1f2

Aliases

arxiv: 0707.0250 · arxiv_version: 0707.0250v4 · doi: 10.48550/arxiv.0707.0250 · pith_short_12: DWG3W47OS6XA · pith_short_16: DWG3W47OS6XA2QG3 · pith_short_8: DWG3W47O

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/DWG3W47OS6XA2QG3BGQCAPIVWL \
  | 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: 1d8dbb73ee97ae0d40db09a0203d15b2fffb6640a549e2dcad705de79225f1f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "724c05ed7484e922e24ef7329169edafc825548062ce6b9919a30a1e0aa1b2b1",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2007-07-02T15:10:06Z",
    "title_canon_sha256": "f1a39dc27d64f47f9a274859dc60c59ba8d5ee67ec46c61e6e7cdcd5b037d695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.0250",
    "kind": "arxiv",
    "version": 4
  }
}