Pith Number

pith:IPI6RGAK

pith:2010:IPI6RGAK6M3YC6XOAKDICU2R6B

not attested not anchored not stored refs pending

The homogenous tree as an electric network

Alice Vatamanelu

arxiv:1007.4565 v1 · 2010-07-26 · 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{IPI6RGAK6M3YC6XOAKDICU2R6B}

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.

Cited by

1 paper in Pith

$p$-Modulus on radially symmetric trees

Receipt and verification

First computed	2026-07-04T17:32:16.956755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43d1e8980af337817aee0286815351f05139a79cb70eb410ece884192d6854e6

Aliases

arxiv: 1007.4565 · arxiv_version: 1007.4565v1 · doi: 10.48550/arxiv.1007.4565 · pith_short_12: IPI6RGAK6M3Y · pith_short_16: IPI6RGAK6M3YC6XO · pith_short_8: IPI6RGAK

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/IPI6RGAK6M3YC6XOAKDICU2R6B \
  | 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: 43d1e8980af337817aee0286815351f05139a79cb70eb410ece884192d6854e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "867c384daddf0911917476975184173515495cb6fc16f213bb9f3cdccc0ed09f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-07-26T20:29:28Z",
    "title_canon_sha256": "2d2e6eca1bdf929dd08975299fe8f9754f1b67c4ec4191c844d2088caec5a76e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4565",
    "kind": "arxiv",
    "version": 1
  }
}