Pith Number

pith:7KHK5FPD

pith:2026:7KHK5FPDI4D32P6SRVTLHBLGEC

not attested not anchored not stored refs pending

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator

Mengyao Zhang

arxiv:2607.05719 v1 · 2026-07-07 · cond-mat.mes-hall

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7KHK5FPDI4D32P6SRVTLHBLGEC}

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.

Cited by

1 paper in Pith

Equivalence between the Axion Invariant and the $S_4$ Symmetry Indicator

Receipt and verification

First computed	2026-07-08T01:18:42.347778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa8eae95e34707bd3fd28d66b385662086fb6f1dc295a0806d9ed7568bdae716

Aliases

arxiv: 2607.05719 · arxiv_version: 2607.05719v1 · doi: 10.48550/arxiv.2607.05719 · pith_short_12: 7KHK5FPDI4D3 · pith_short_16: 7KHK5FPDI4D32P6S · pith_short_8: 7KHK5FPD

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/7KHK5FPDI4D32P6SRVTLHBLGEC \
  | 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: fa8eae95e34707bd3fd28d66b385662086fb6f1dc295a0806d9ed7568bdae716

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "835f4a2b6ac4b3c1f8714f0fbd85ed1ae14afa42f778d628bb5010e86acaf175",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cond-mat.mes-hall",
    "submitted_at": "2026-07-07T01:03:40Z",
    "title_canon_sha256": "d9a9a638eee372f24db17234c7d8ec44c5c3add6a07c4a9a77f0a6fb49a04be7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05719",
    "kind": "arxiv",
    "version": 1
  }
}