Pith Number

pith:DSVHD4X7

pith:2016:DSVHD4X77AJ2PGCCB23EMEQY77

not attested not anchored not stored refs pending

A note on continuity of magnetization at criticality for the ferromagnetic Ising model on amenable quasi-transitive graphs with exponential growth

Aran Raoufi

arxiv:1606.03763 v1 · 2016-06-12 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DSVHD4X77AJ2PGCCB23EMEQY77}

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	2026-05-18T01:12:33.100112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1caa71f2fff813a798420eb6461218ffdf0953ea52b081ef3869b8404565329f

Aliases

arxiv: 1606.03763 · arxiv_version: 1606.03763v1 · doi: 10.48550/arxiv.1606.03763 · pith_short_12: DSVHD4X77AJ2 · pith_short_16: DSVHD4X77AJ2PGCC · pith_short_8: DSVHD4X7

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/DSVHD4X77AJ2PGCCB23EMEQY77 \
  | 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: 1caa71f2fff813a798420eb6461218ffdf0953ea52b081ef3869b8404565329f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78db4c88bdc2a2462c2bab97f817e0beea63b183f08c37f261fe50a49237d904",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-12T20:38:46Z",
    "title_canon_sha256": "1d88cf587e83236fa6d34593b70aa13c1ceca445285ac4aac519ef29ecdd3224"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03763",
    "kind": "arxiv",
    "version": 1
  }
}