Pith Number

pith:WKKWXNCP

pith:2026:WKKWXNCPHKJ34UF2THKBDTDFKE

not attested not anchored not stored refs pending

Symmetry-Twisted Multi-Entropies: Order Parameters for 2D SPT Phases

Michael Levin, Ramanjit Sohal, Ruben Verresen

arxiv:2607.12023 v1 · 2026-07-13 · cond-mat.str-el · hep-th · 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{WKKWXNCPHKJ34UF2THKBDTDFKE}

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	2026-07-15T00:21:28.491831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2956bb44f3a93be50ba99d411cc65511d36e6b81cfa90203e311f043a0e711f

Aliases

arxiv: 2607.12023 · arxiv_version: 2607.12023v1 · doi: 10.48550/arxiv.2607.12023 · pith_short_12: WKKWXNCPHKJ3 · pith_short_16: WKKWXNCPHKJ34UF2 · pith_short_8: WKKWXNCP

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/WKKWXNCPHKJ34UF2THKBDTDFKE \
  | 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: b2956bb44f3a93be50ba99d411cc65511d36e6b81cfa90203e311f043a0e711f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f145b5351b34eb19344efea9e83ad4c402da6a2fbe3fefe7c8e6cfca3b8d4746",
    "cross_cats_sorted": [
      "hep-th",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-07-13T18:00:01Z",
    "title_canon_sha256": "cb57675558277d401e6bab7482e1ed3eac5fdee52d2c4aea7bf3e67b5da9a882"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12023",
    "kind": "arxiv",
    "version": 1
  }
}