Pith Number

pith:KWKA2QFD

pith:2009:KWKA2QFDMG7A5F2CUIUBGZ6GEJ

not attested not anchored not stored refs pending

A product involving the $\beta$-family in stable homotopy theory

Wending Li, Xiugui Liu

arxiv:0911.1093 v1 · 2009-11-05 · 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{KWKA2QFDMG7A5F2CUIUBGZ6GEJ}

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	2026-05-18T04:41:35.887475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55940d40a361be0e9742a2281367c622744a7042de0e0f9122d386fdefea3e6c

Aliases

arxiv: 0911.1093 · arxiv_version: 0911.1093v1 · doi: 10.48550/arxiv.0911.1093 · pith_short_12: KWKA2QFDMG7A · pith_short_16: KWKA2QFDMG7A5F2C · pith_short_8: KWKA2QFD

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/KWKA2QFDMG7A5F2CUIUBGZ6GEJ \
  | 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: 55940d40a361be0e9742a2281367c622744a7042de0e0f9122d386fdefea3e6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2abbf402380caa894b906f04947c14dd4bba54470b8e216b5fbe0cb5246e2140",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-11-05T18:21:38Z",
    "title_canon_sha256": "b1d58776f48f4de15c97a19e5c86c1ad0ba25c35fc5d0b1e1b791c213cf8dc38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1093",
    "kind": "arxiv",
    "version": 1
  }
}