Pith Number

pith:SYGUJ5Y5

pith:2021:SYGUJ5Y5IGAPX5EAC6EBHYQCGA

not attested not anchored not stored refs pending

From Torus Bundles to Particle-Hole Equivariantization

Paul Gustafson, Qing Zhang, Shawn X. Cui, Yang Qiu

arxiv:2106.01959 v3 · 2021-06-03 · math.QA · math-ph · math.GT · math.MP · 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{SYGUJ5Y5IGAPX5EAC6EBHYQCGA}

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	2026-07-05T05:01:15.419836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

960d44f71d4180fbf480178813e2023029d0bd9b947e172b775f43cd3942ee88

Aliases

arxiv: 2106.01959 · arxiv_version: 2106.01959v3 · doi: 10.48550/arxiv.2106.01959 · pith_short_12: SYGUJ5Y5IGAP · pith_short_16: SYGUJ5Y5IGAPX5EA · pith_short_8: SYGUJ5Y5

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/SYGUJ5Y5IGAPX5EAC6EBHYQCGA \
  | 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: 960d44f71d4180fbf480178813e2023029d0bd9b947e172b775f43cd3942ee88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93f67d2dfaffb3c426929833ef8a3a91c5514cad4aed7c6c69aea4fe38242dee",
    "cross_cats_sorted": [
      "math-ph",
      "math.GT",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2021-06-03T16:06:26Z",
    "title_canon_sha256": "99a999ef0031ffd6eb440af4ef0cc161178e3f93422321fed3c81acb31e7b4bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.01959",
    "kind": "arxiv",
    "version": 3
  }
}