Pith Number

pith:KB3T7W4F

pith:2012:KB3T7W4FMGTZQMQUBX5IFYTKKK

not attested not anchored not stored refs pending

On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators

Moritz Gerlach

arxiv:1201.3531 v2 · 2012-01-17 · 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{KB3T7W4FMGTZQMQUBX5IFYTKKK}

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	2026-05-18T03:15:43.996699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50773fdb8561a79832140dfa82e26a52b725970822c8d4d1db3a166f7a95d076

Aliases

arxiv: 1201.3531 · arxiv_version: 1201.3531v2 · doi: 10.48550/arxiv.1201.3531 · pith_short_12: KB3T7W4FMGTZ · pith_short_16: KB3T7W4FMGTZQMQU · pith_short_8: KB3T7W4F

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/KB3T7W4FMGTZQMQUBX5IFYTKKK \
  | 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: 50773fdb8561a79832140dfa82e26a52b725970822c8d4d1db3a166f7a95d076

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2c3e310ea7b645f6121c452ba8da41fda8fbac9aa38e27bcadf5978222a4bfd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-01-17T15:35:20Z",
    "title_canon_sha256": "39760544266ce24398287f7123132c87e9fddc6ee052825b0d9d7d79cd27c0d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3531",
    "kind": "arxiv",
    "version": 2
  }
}