Pith Number

pith:DLOTFCNZ

pith:2026:DLOTFCNZMBYCZED3LNDGIDH2CA

not attested not anchored not stored refs pending

Essential spectrum for Brox-type diffusion processes

Jian Wang, Yuichi Shiozawa

arxiv:2607.07410 v1 · 2026-07-08 · math.PR · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DLOTFCNZMBYCZED3LNDGIDH2CA}

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	2026-07-09T01:20:24.225518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1add3289b960702c907b5b46640cfa10206edd78d866cc451f7fc4c148153996

Aliases

arxiv: 2607.07410 · arxiv_version: 2607.07410v1 · doi: 10.48550/arxiv.2607.07410 · pith_short_12: DLOTFCNZMBYC · pith_short_16: DLOTFCNZMBYCZED3 · pith_short_8: DLOTFCNZ

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/DLOTFCNZMBYCZED3LNDGIDH2CA \
  | 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: 1add3289b960702c907b5b46640cfa10206edd78d866cc451f7fc4c148153996

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38e4e39f1d6f09c6eef90376f445bd37bc19499a64b93ca7b087c170fd2c87d2",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-08T13:42:27Z",
    "title_canon_sha256": "00142e9b5f7c640cdba975de03d197afc64f77841a761adee774b6fccf3bee92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07410",
    "kind": "arxiv",
    "version": 1
  }
}