Pith Number

pith:DMHWARMJ

pith:2025:DMHWARMJ5L4IO3HZP3TJGBXLCY

not attested not anchored not stored refs pending

Fractional multi-phase transitions and nonlocal minimal partitions

Thomas Gabard, Vincent Millot

arxiv:2506.20226 v1 · 2025-06-25 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DMHWARMJ5L4IO3HZP3TJGBXLCY}

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	2026-07-05T11:27:14.775284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b0f604589eaf8876cf97ee69306eb162372cae4ab42e7a5c163d6e80aa7ecbc

Aliases

arxiv: 2506.20226 · arxiv_version: 2506.20226v1 · doi: 10.48550/arxiv.2506.20226 · pith_short_12: DMHWARMJ5L4I · pith_short_16: DMHWARMJ5L4IO3HZ · pith_short_8: DMHWARMJ

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/DMHWARMJ5L4IO3HZP3TJGBXLCY \
  | 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: 1b0f604589eaf8876cf97ee69306eb162372cae4ab42e7a5c163d6e80aa7ecbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9f2e91e0dfdae5d6be6bd253b2a187364e63bc1773836d440b7779236a4a09b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-25T08:15:44Z",
    "title_canon_sha256": "28e13cc416f9d96f56a48c0880de884325a8d51d39e196b6935b056c7b5aa980"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.20226",
    "kind": "arxiv",
    "version": 1
  }
}