Pith Number

pith:Y5OGPNBT

pith:2023:Y5OGPNBTVA46WHZM246DG7FRG7

not attested not anchored not stored refs resolved

Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups

Ken Shiozaki, Seishiro Ono

The Atiyah-Hirzebruch spectral sequence determines the topological K-groups for about 59 percent of three-dimensional magnetic space group settings.

arxiv:2304.01827 v2 · 2023-04-04 · cond-mat.mes-hall · cond-mat.supr-con

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5OGPNBTVA46WHZM246DG7FRG7}

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.

Claims

C1strongest claim

We determine the K-groups for approximately 59% of symmetry settings in three spatial dimensions.

C2weakest assumption

Under a physically reasonable assumption, we enumerate all possible K-groups that are compatible with the E2 pages for both momentum and real-space AHSS.

C3one line summary

Computes E2 pages of momentum- and real-space AHSS for 1651 magnetic space groups and determines compatible K-groups for ~59% of 3D symmetry settings under a physical assumption.

References

74 extracted · 74 resolved · 1 Pith anchors

[1] ch shφh φhch sh ch shφh φhch sh TABLE I

[2] (75) We note that since the p-cells inCp are oriented sym- metrically, there is no sign change due to the mismatch of orientations

[3] crys- talline topological liquid

[4] Pick a representative p-cell Dp i of an or- bit of equivalent p-cells inCp

[5] Z2 classiﬁcation For an irrep αr(xp i ), if the classiﬁcation of degree −n is Z2, set bp,−n ir = dim (H), the matrix dimension listed in Table II. For other equivalent irreps h[α(xp i )] at h(x)∈ X, s

Cited by

1 paper in Pith

Towards complete characterization of topological insulators and superconductors: A systematic construction of topological invariants based on Atiyah-Hirzebruch spectral sequence

Receipt and verification

First computed	2026-06-01T01:02:11.141554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c75c67b433a839eb1f2cd73c337cb137e6873ddb5ed46dba33e2cf06ea0477a8

Aliases

arxiv: 2304.01827 · arxiv_version: 2304.01827v2 · doi: 10.48550/arxiv.2304.01827 · pith_short_12: Y5OGPNBTVA46 · pith_short_16: Y5OGPNBTVA46WHZM · pith_short_8: Y5OGPNBT

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/Y5OGPNBTVA46WHZM246DG7FRG7 \
  | 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: c75c67b433a839eb1f2cd73c337cb137e6873ddb5ed46dba33e2cf06ea0477a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e54f5705f6eac6e71503c6c1b6f9abcdd1d482e7b4deff747a8e0197f36f927",
    "cross_cats_sorted": [
      "cond-mat.supr-con"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mes-hall",
    "submitted_at": "2023-04-04T14:31:20Z",
    "title_canon_sha256": "acc32a7097ff25f74930ec964e92836fd98038e8b534a9ceb1d4bdc046231b01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.01827",
    "kind": "arxiv",
    "version": 2
  }
}