Pith Number

pith:PUJBKPJ6

pith:2013:PUJBKPJ6YYFQBF6TYJDFSHDB5X

not attested not anchored not stored refs pending

Variational principles for topological pressures on subsets

Wen-Chiao Cheng, Xinjia Tang, Yun Zhao

arxiv:1308.0445 v1 · 2013-08-02 · 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{PUJBKPJ6YYFQBF6TYJDFSHDB5X}

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	2026-05-18T03:16:50.467706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d12153d3ec60b0097d3c246591c61edd09fabd3967960dd419c4474f13135bb

Aliases

arxiv: 1308.0445 · arxiv_version: 1308.0445v1 · doi: 10.48550/arxiv.1308.0445 · pith_short_12: PUJBKPJ6YYFQ · pith_short_16: PUJBKPJ6YYFQBF6T · pith_short_8: PUJBKPJ6

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/PUJBKPJ6YYFQBF6TYJDFSHDB5X \
  | 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: 7d12153d3ec60b0097d3c246591c61edd09fabd3967960dd419c4474f13135bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8cd071922f55575d636916a78eb74bb60958a1a6867283a9848dad5014de929",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-08-02T09:23:57Z",
    "title_canon_sha256": "744e0f779a756c40df3273283f35d98f2a5869156526a511066e65ec093d1f0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.0445",
    "kind": "arxiv",
    "version": 1
  }
}