Pith Number

pith:XCFXSM4C

pith:2005:XCFXSM4CNGTFGMWM67X5BZRRTK

not attested not anchored not stored refs pending

Isometric group actions on Hilbert spaces: growth of cocycles

Alain Valette, Romain Tessera, Yves de Cornulier

arxiv:math/0509527 v2 · 2005-09-22 · math.GR · 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{XCFXSM4CNGTFGMWM67X5BZRRTK}

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	2026-05-18T04:42:36.328475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b88b79338269a65332ccf7efd0e6319ab106148f28f577e157a7350fa04bce8d

Aliases

arxiv: math/0509527 · arxiv_version: math/0509527v2 · doi: 10.48550/arxiv.math/0509527 · pith_short_12: XCFXSM4CNGTF · pith_short_16: XCFXSM4CNGTFGMWM · pith_short_8: XCFXSM4C

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/XCFXSM4CNGTFGMWM67X5BZRRTK \
  | 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: b88b79338269a65332ccf7efd0e6319ab106148f28f577e157a7350fa04bce8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e0de5e3956f5161a7a4106a706dc72534d42b98bc9e7ff9d8f01b08974e26a8",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-09-22T17:55:26Z",
    "title_canon_sha256": "2f04074f7f17460e8e3b883a0cb2d1a80b57b6a289d0a55eeeb66da9d4161f6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509527",
    "kind": "arxiv",
    "version": 2
  }
}