Pith Number

pith:KMRPGROW

pith:2021:KMRPGROWCUSLJH4DCJEYZIQH2P

not attested not anchored not stored refs pending

Presentation of the fundamental groups of complements of shadows

Hironobu Naoe, Masaharu Ishikawa, Yuya Koda

arxiv:2110.02431 v3 · 2021-10-06 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KMRPGROWCUSLJH4DCJEYZIQH2P}

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	2026-07-05T04:38:45.023117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5322f345d61524b49f8312498ca207d3e73645c1aaccbde7b000656a5717497d

Aliases

arxiv: 2110.02431 · arxiv_version: 2110.02431v3 · doi: 10.48550/arxiv.2110.02431 · pith_short_12: KMRPGROWCUSL · pith_short_16: KMRPGROWCUSLJH4D · pith_short_8: KMRPGROW

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/KMRPGROWCUSLJH4DCJEYZIQH2P \
  | 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: 5322f345d61524b49f8312498ca207d3e73645c1aaccbde7b000656a5717497d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb9f77511d2f38aae8d0fa603b263bd5d22ac8681a25fde677354f4ef70cd66a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-10-06T00:43:12Z",
    "title_canon_sha256": "bfcdc05397877e25c960e02597b55334402c49f51d76481819307be54ccd1f5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.02431",
    "kind": "arxiv",
    "version": 3
  }
}