Pith Number

pith:5UOZHYB2

pith:2005:5UOZHYB2GFOYIBKLMSHVLXHOWD

not attested not anchored not stored refs pending

The spectrum of the averaging operator on a network (metric graph)

Donald I. Cartwright, Wolfgang Woess

arxiv:math/0509595 v1 · 2005-09-26 · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UOZHYB2GFOYIBKLMSHVLXHOWD}

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	2026-05-18T03:39:14.969330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed1d93e03a315d84054b648f55dceeb0e59d3c4b29f94c0a4bc3a697f211d23d

Aliases

arxiv: math/0509595 · arxiv_version: math/0509595v1 · doi: 10.48550/arxiv.math/0509595 · pith_short_12: 5UOZHYB2GFOY · pith_short_16: 5UOZHYB2GFOYIBKL · pith_short_8: 5UOZHYB2

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/5UOZHYB2GFOYIBKLMSHVLXHOWD \
  | 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: ed1d93e03a315d84054b648f55dceeb0e59d3c4b29f94c0a4bc3a697f211d23d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1559439dfaf2a2f5e05a137c84f3c9285014d4b074a62d63c4c76e8d76fb03dc",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2005-09-26T07:42:14Z",
    "title_canon_sha256": "15f46aed5bd94a8b985ffbc5af574122b479e6202e733adf0bfcdcb6da3beb91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509595",
    "kind": "arxiv",
    "version": 1
  }
}