Pith Number

pith:HPQ5JQJ6

pith:2026:HPQ5JQJ6ZAWHDG6IEAESVGBLSM

not attested not anchored not stored refs pending

Subcritical sharpness for real-valued spin models

Christoforos Panagiotis, William Veitch

arxiv:2605.31344 v1 · 2026-05-29 · 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{HPQ5JQJ6ZAWHDG6IEAESVGBLSM}

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	2026-06-01T02:03:59.883303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3be1d4c13ec82c719bc820092a982b932735a8624fa186bafd5855247d5e8a4b

Aliases

arxiv: 2605.31344 · arxiv_version: 2605.31344v1 · doi: 10.48550/arxiv.2605.31344 · pith_short_12: HPQ5JQJ6ZAWH · pith_short_16: HPQ5JQJ6ZAWHDG6I · pith_short_8: HPQ5JQJ6

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/HPQ5JQJ6ZAWHDG6IEAESVGBLSM \
  | 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: 3be1d4c13ec82c719bc820092a982b932735a8624fa186bafd5855247d5e8a4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c011a928e618b278a0a88bbaeaf61c59ed8bb9361cfce2e26887c2cfa4b48d3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-29T14:22:21Z",
    "title_canon_sha256": "3b63f3f81bdf1d9d764b09ebdc22d8698fedac60524c97452626cbde3a3eb1ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.31344",
    "kind": "arxiv",
    "version": 1
  }
}