Pith Number

pith:WHKDOHD7

pith:2026:WHKDOHD7MZLW4UKA3Q7D3DRCZP

not attested not anchored not stored refs pending

Thermodynamic formalism for non-compact systems with expansivity and specification

Daniel J. Thompson, Tianyu Wang, Vaughn Climenhaga

arxiv:2606.20405 v1 · 2026-06-18 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WHKDOHD7MZLW4UKA3Q7D3DRCZP}

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	2026-06-19T16:13:11.725578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1d4371c7f66576e5140dc3e3d8e22cbfc9876c003e15b014b0f92917e3fd079

Aliases

arxiv: 2606.20405 · arxiv_version: 2606.20405v1 · doi: 10.48550/arxiv.2606.20405 · pith_short_12: WHKDOHD7MZLW · pith_short_16: WHKDOHD7MZLW4UKA · pith_short_8: WHKDOHD7

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/WHKDOHD7MZLW4UKA3Q7D3DRCZP \
  | 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: b1d4371c7f66576e5140dc3e3d8e22cbfc9876c003e15b014b0f92917e3fd079

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "580000f4a59f89a0591c3567de04362350a8948d624289f863c0cabf7892d0c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-18T15:56:13Z",
    "title_canon_sha256": "f8102052dea7dab2872c2f4f8954283c8ef62f385a4c9fc7f6e12db6854df29b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20405",
    "kind": "arxiv",
    "version": 1
  }
}