Pith Number

pith:76KIMX66

pith:2013:76KIMX66CQFKVO3VPWY7NHALBQ

not attested not anchored not stored refs pending

Negative definite functions and a dynamical characterization of property (T) for countable groups

Guyan Robertson, Tim Steger

arxiv:1302.5789 v1 · 2013-02-23 · 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{76KIMX66CQFKVO3VPWY7NHALBQ}

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	2026-05-18T03:32:43.750878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff94865fde140aaabb757db1f69c0b0c399ff3cf80b796550f3954cdae181334

Aliases

arxiv: 1302.5789 · arxiv_version: 1302.5789v1 · doi: 10.48550/arxiv.1302.5789 · pith_short_12: 76KIMX66CQFK · pith_short_16: 76KIMX66CQFKVO3V · pith_short_8: 76KIMX66

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/76KIMX66CQFKVO3VPWY7NHALBQ \
  | 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: ff94865fde140aaabb757db1f69c0b0c399ff3cf80b796550f3954cdae181334

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b8e5f7c764515b73b703992da740e7711c81af09bf31a0d608f67cf126bd09f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-02-23T12:03:24Z",
    "title_canon_sha256": "afcf28d0fc45dde1ddd9bf1f967691f7a8b1f24ac2f5647da7eb249b15db25fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5789",
    "kind": "arxiv",
    "version": 1
  }
}