Pith Number

pith:A4IWEBQK

pith:2006:A4IWEBQKK4S36ILE63TQ4ROUOI

not attested not anchored not stored refs pending

The 1-type of a Waldhausen K-theory spectrum

Andrew Tonks, Fernando Muro

arxiv:math/0603544 v3 · 2006-03-22 · math.KT · 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{A4IWEBQKK4S36ILE63TQ4ROUOI}

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	2026-05-18T04:08:53.542188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

071162060a5725bf2164f6e70e45d4723afdd00659c49f98648c1120f6ed4517

Aliases

arxiv: math/0603544 · arxiv_version: math/0603544v3 · doi: 10.48550/arxiv.math/0603544 · pith_short_12: A4IWEBQKK4S3 · pith_short_16: A4IWEBQKK4S36ILE · pith_short_8: A4IWEBQK

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/A4IWEBQKK4S36ILE63TQ4ROUOI \
  | 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: 071162060a5725bf2164f6e70e45d4723afdd00659c49f98648c1120f6ed4517

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbf204707bd13478b91fb636211d8496e6192f51206a58102df9b42fe358ac06",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.KT",
    "submitted_at": "2006-03-22T20:13:53Z",
    "title_canon_sha256": "f50b7a36697de7b1a68a7d61af11d9b1dad83c5b80484b89e19d4d18a95c57c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0603544",
    "kind": "arxiv",
    "version": 3
  }
}