Pith Number

pith:I5AYO2U7

pith:2026:I5AYO2U7GNYKLRLE47L7LJ5KPH

not attested not anchored not stored refs pending

Entanglement-spectrum fingerprint of a non-invertible symmetry: the Kramers--Wannier duality defect on the lattice

Yi Liang

arxiv:2607.01137 v1 · 2026-07-01 · 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{I5AYO2U7GNYKLRLE47L7LJ5KPH}

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	2026-07-02T01:18:30.121827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4741876a9f3370a5c564e7d7f5a7aa79f110969e440ced8ddf11e9bdac08112e

Aliases

arxiv: 2607.01137 · arxiv_version: 2607.01137v1 · doi: 10.48550/arxiv.2607.01137 · pith_short_12: I5AYO2U7GNYK · pith_short_16: I5AYO2U7GNYKLRLE · pith_short_8: I5AYO2U7

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/I5AYO2U7GNYKLRLE47L7LJ5KPH \
  | 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: 4741876a9f3370a5c564e7d7f5a7aa79f110969e440ced8ddf11e9bdac08112e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c201239e3b9f0cc155a7f0d6a54e2c40545a554e476f979f3ff6ec33cb40501",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-01T16:21:58Z",
    "title_canon_sha256": "e92e54fd325a447a13ae22a330cdaf36ebdac8cf1c7baa75634e4515402d23d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01137",
    "kind": "arxiv",
    "version": 1
  }
}