Pith Number

pith:NVJQCIES

pith:2026:NVJQCIESVOBHVL3ITMLZPWTZCN

not attested not anchored not stored refs pending

Shallow Unitary Circuits for Kramers-Wannier Dualities

Shang Liu, Yanting Cheng

arxiv:2607.01624 v1 · 2026-07-02 · quant-ph · cond-mat.quant-gas · cond-mat.str-el

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NVJQCIESVOBHVL3ITMLZPWTZCN}

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	2026-07-03T01:17:03.682835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d53012092ab827aaf689b1797da79135c1ec990a758b1091e67416083dc55b5

Aliases

arxiv: 2607.01624 · arxiv_version: 2607.01624v1 · doi: 10.48550/arxiv.2607.01624 · pith_short_12: NVJQCIESVOBH · pith_short_16: NVJQCIESVOBHVL3I · pith_short_8: NVJQCIES

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/NVJQCIESVOBHVL3ITMLZPWTZCN \
  | 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: 6d53012092ab827aaf689b1797da79135c1ec990a758b1091e67416083dc55b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9dd6974ccead5107b8eb37044727bd88d6a39b5d06e0258c350fa4940281391",
    "cross_cats_sorted": [
      "cond-mat.quant-gas",
      "cond-mat.str-el"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-02T02:44:27Z",
    "title_canon_sha256": "032fd4469c03ad2cf1e7e6e421876e0a8b498ce0fa77db366319f1f116aa850e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01624",
    "kind": "arxiv",
    "version": 1
  }
}