Pith Number

pith:6PVTVKNJ

pith:2015:6PVTVKNJZEVSF4M2SMDWAXEWWY

not attested not anchored not stored refs pending

Non-commutativity of exponential spectrum

Hubert Klaja, Thomas Ransford

arxiv:1510.08109 v2 · 2015-10-27 · math.FA · 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{6PVTVKNJZEVSF4M2SMDWAXEWWY}

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	2026-05-18T01:26:09.267926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3eb3aa9a9c92b22f19a9307605c96b63f0d48dd13ec09baeca1984ec2c06d50

Aliases

arxiv: 1510.08109 · arxiv_version: 1510.08109v2 · doi: 10.48550/arxiv.1510.08109 · pith_short_12: 6PVTVKNJZEVS · pith_short_16: 6PVTVKNJZEVSF4M2 · pith_short_8: 6PVTVKNJ

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/6PVTVKNJZEVSF4M2SMDWAXEWWY \
  | 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: f3eb3aa9a9c92b22f19a9307605c96b63f0d48dd13ec09baeca1984ec2c06d50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad00be940917d7c82e97fff5a93486af04fc552dd2006c8cd2fcfd5888ac6f03",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-10-27T22:04:36Z",
    "title_canon_sha256": "bf47e729dcf67d350407f112429c4468b329113a65076413a94732bc71eafe94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08109",
    "kind": "arxiv",
    "version": 2
  }
}