Pith Number

pith:GC7TRPOD

pith:2005:GC7TRPOD65H5YUCUBLCRJRQZ64

not attested not anchored not stored refs pending

Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs

Sara Brofferio, Wolfgang Woess

arxiv:math/0501440 v1 · 2005-01-25 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GC7TRPOD65H5YUCUBLCRJRQZ64}

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	2026-05-18T03:39:14.980132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30bf38bdc3f74fdc50540ac514c619f73d2d769df988a84ef8e8c30582ed8f58

Aliases

arxiv: math/0501440 · arxiv_version: math/0501440v1 · doi: 10.48550/arxiv.math/0501440 · pith_short_12: GC7TRPOD65H5 · pith_short_16: GC7TRPOD65H5YUCU · pith_short_8: GC7TRPOD

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/GC7TRPOD65H5YUCUBLCRJRQZ64 \
  | 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: 30bf38bdc3f74fdc50540ac514c619f73d2d769df988a84ef8e8c30582ed8f58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a7ee369307efcac3d9bd9d7351cd93b687e9fd54814482aac82f214909b8013",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-01-25T10:41:20Z",
    "title_canon_sha256": "bad95dc4a810cfd83cba3986cf51650ae558fb6a6a00486d7f200338421746cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501440",
    "kind": "arxiv",
    "version": 1
  }
}