Pith Number

pith:VNQGR55I

pith:2011:VNQGR55IXQIIN4NLHXWW2RFS5D

not attested not anchored not stored refs pending

The Pascal automorphism has a purely continuous spectrum

A.Vershik

arxiv:1103.4898 v3 · 2011-03-25 · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VNQGR55IXQIIN4NLHXWW2RFS5D}

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	2026-05-18T04:14:27.489888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab6068f7a8bc1086f1ab3ded6d44b2e8cd9271815a5ca4ebddbefb0f796d2969

Aliases

arxiv: 1103.4898 · arxiv_version: 1103.4898v3 · doi: 10.48550/arxiv.1103.4898 · pith_short_12: VNQGR55IXQII · pith_short_16: VNQGR55IXQIIN4NL · pith_short_8: VNQGR55I

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/VNQGR55IXQIIN4NLHXWW2RFS5D \
  | 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: ab6068f7a8bc1086f1ab3ded6d44b2e8cd9271815a5ca4ebddbefb0f796d2969

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cdab1e011b4e4fea37fa51f9fb18caca8bf867061edec2dadd9da14f524d879",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-25T03:08:58Z",
    "title_canon_sha256": "29ba3c8fc26b429a487efa5ddebe1a35d4027d2517cdd793b6d0ec8827a69dc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4898",
    "kind": "arxiv",
    "version": 3
  }
}