Pith Number

pith:Q5LWV274

pith:2016:Q5LWV274IACMDXICHBM2PG5AUW

not attested not anchored not stored refs pending

Minkowski dimension and explicit tube formulas for $p$-adic fractal strings

L\~u' H\`ung, Machiel van Frankenhuijsen, Michel L. Lapidus

arxiv:1603.09409 v4 · 2016-03-30 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q5LWV274IACMDXICHBM2PG5AUW}

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	2026-05-18T00:03:34.579009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87576aebfc4004c1dd023859a79ba0a58e7c310354113e66628cc176b7783462

Aliases

arxiv: 1603.09409 · arxiv_version: 1603.09409v4 · doi: 10.48550/arxiv.1603.09409 · pith_short_12: Q5LWV274IACM · pith_short_16: Q5LWV274IACMDXIC · pith_short_8: Q5LWV274

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/Q5LWV274IACMDXICHBM2PG5AUW \
  | 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: 87576aebfc4004c1dd023859a79ba0a58e7c310354113e66628cc176b7783462

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4693ca1c82bfc2dcc1bc18a23417a69a8f9138f286cb4b5626a2f32cc074dfa4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-03-30T22:53:36Z",
    "title_canon_sha256": "373600927a1e4bee53a5718be67dc33ee4a9b81a9d0ed317527cb7e6c28e4a72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.09409",
    "kind": "arxiv",
    "version": 4
  }
}