Pith Number

pith:JPRZFPJS

pith:2016:JPRZFPJSWMRHKLA2Z7PAXLQ3LQ

not attested not anchored not stored refs pending

Phase transitions in long-range Ising models and an optimal condition for factors of $g$-measures

Anders Johansson, Anders \"Oberg, Mark Pollicott

arxiv:1611.04547 v2 · 2016-11-14 · 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{JPRZFPJSWMRHKLA2Z7PAXLQ3LQ}

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	2026-05-18T00:43:09.040675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4be392bd32b322752c1acfde0bae1b5c0fb69082de0dcdff03abad31f082cb4f

Aliases

arxiv: 1611.04547 · arxiv_version: 1611.04547v2 · doi: 10.48550/arxiv.1611.04547 · pith_short_12: JPRZFPJSWMRH · pith_short_16: JPRZFPJSWMRHKLA2 · pith_short_8: JPRZFPJS

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/JPRZFPJSWMRHKLA2Z7PAXLQ3LQ \
  | 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: 4be392bd32b322752c1acfde0bae1b5c0fb69082de0dcdff03abad31f082cb4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "298131add6aeab0aa1f191317d00954a9eccfb709d50125fee63d2f448c1711d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-11-14T20:11:32Z",
    "title_canon_sha256": "aa05f00dddb77088ec7e07e103e6da5177354ee10ea99c2d8f2d58a372fb18cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04547",
    "kind": "arxiv",
    "version": 2
  }
}