Pith Number

pith:563F7R5Y

pith:2015:563F7R5Y4QVKAH2CJQYI64YYBE

not attested not anchored not stored refs pending

On the sharpness of a three circles theorem for discrete harmonic functions

Dan Mangoubi, Gabor Lippner

arxiv:1512.03732 v1 · 2015-12-03 · math.CA · math.AP · 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{563F7R5Y4QVKAH2CJQYI64YYBE}

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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

A Liouville principle for the random conductance model under degenerate conditions

Receipt and verification

First computed	2026-07-04T23:50:10.243352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efb65fc7b8e42aa01f424c308f7318092ce54aca0bc7b6a8d5a875f2eed7c82f

Aliases

arxiv: 1512.03732 · arxiv_version: 1512.03732v1 · doi: 10.48550/arxiv.1512.03732 · pith_short_12: 563F7R5Y4QVK · pith_short_16: 563F7R5Y4QVKAH2C · pith_short_8: 563F7R5Y

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/563F7R5Y4QVKAH2CJQYI64YYBE \
  | 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: efb65fc7b8e42aa01f424c308f7318092ce54aca0bc7b6a8d5a875f2eed7c82f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7ea499e7e7f5ec496d68a57481fb75875b630bbabfdbebf47c100a3ef89ef24",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-03T14:29:49Z",
    "title_canon_sha256": "872655598bd1215668b481280e9e99e722f6cbecc8dec9dc35f5817d6380ed1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03732",
    "kind": "arxiv",
    "version": 1
  }
}