Pith Number

pith:G4UMYKK6

pith:2018:G4UMYKK6ZDZ4CCBZ7FUTMD2N24

not attested not anchored not stored refs pending

Commuting matrices and Atiyah's Real K-theory

Markus Hausmann, Simon Gritschacher

arxiv:1807.06864 v2 · 2018-07-18 · 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{G4UMYKK6ZDZ4CCBZ7FUTMD2N24}

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	2026-05-17T23:47:59.774677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3728cc295ec8f3c10839f969360f4dd7342f1b4fc062f10ed3cdef2eb49fea58

Aliases

arxiv: 1807.06864 · arxiv_version: 1807.06864v2 · doi: 10.48550/arxiv.1807.06864 · pith_short_12: G4UMYKK6ZDZ4 · pith_short_16: G4UMYKK6ZDZ4CCBZ · pith_short_8: G4UMYKK6

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/G4UMYKK6ZDZ4CCBZ7FUTMD2N24 \
  | 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: 3728cc295ec8f3c10839f969360f4dd7342f1b4fc062f10ed3cdef2eb49fea58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd3dc58998a387d70bad8234a97aa70c75172a5665642cfa86158094478adaed",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-07-18T11:09:47Z",
    "title_canon_sha256": "4a753fcebe6deea4ce016c8e39f1b33b5162e125b50826de75e77f8646aa5d34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.06864",
    "kind": "arxiv",
    "version": 2
  }
}