Pith Number

pith:Y4LDKYIC

pith:2026:Y4LDKYICZ5TP3YU34MLEYPZVTW

not attested not anchored not stored refs pending

Twin Phases: Phase Transitions Without Hidden Symmetry Breaking

Alison Warman, Sakura Schafer-Nameki, Yuhan Gai

arxiv:2605.31601 v1 · 2026-05-29 · cond-mat.str-el · hep-th · math.CT · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y4LDKYICZ5TP3YU34MLEYPZVTW}

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	2026-06-01T02:04:15.228768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c716356102cf66fde29be3164c3f359d95081319793a432580bc7998d0b6d118

Aliases

arxiv: 2605.31601 · arxiv_version: 2605.31601v1 · doi: 10.48550/arxiv.2605.31601 · pith_short_12: Y4LDKYICZ5TP · pith_short_16: Y4LDKYICZ5TP3YU3 · pith_short_8: Y4LDKYIC

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/Y4LDKYICZ5TP3YU34MLEYPZVTW \
  | 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: c716356102cf66fde29be3164c3f359d95081319793a432580bc7998d0b6d118

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f20f31049a02edb506d8c4c374f585a0c8057317a04edfd89bf73aed6e8d1c16",
    "cross_cats_sorted": [
      "hep-th",
      "math.CT",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-05-29T17:59:38Z",
    "title_canon_sha256": "7f413c90012e056e94de7d28c21936e5c5670cde8ce1bbf8c2a303691ba144b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.31601",
    "kind": "arxiv",
    "version": 1
  }
}