Pith Number

pith:RGND6KNB

pith:2021:RGND6KNB2UK5FX2SOSTMTQGDCU

not attested not anchored not stored refs pending

Girth, magnitude homology, and phase transition of diagonality

Shu Kanazawa, Yasuaki Hiraoka, Yasuhiko Asao

arxiv:2101.09044 v2 · 2021-01-22 · math.AT · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RGND6KNB2UK5FX2SOSTMTQGDCU}

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	2026-07-05T02:14:00.242777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

899a3f29a1d515d2df5274a6c9c0c3153635804429f1f8a2866013f974de60bf

Aliases

arxiv: 2101.09044 · arxiv_version: 2101.09044v2 · doi: 10.48550/arxiv.2101.09044 · pith_short_12: RGND6KNB2UK5 · pith_short_16: RGND6KNB2UK5FX2S · pith_short_8: RGND6KNB

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/RGND6KNB2UK5FX2SOSTMTQGDCU \
  | 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: 899a3f29a1d515d2df5274a6c9c0c3153635804429f1f8a2866013f974de60bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8f0c2d82231baee8f46f8836746e7387e3d69e2f886a6e7516ec60eb051426f",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2021-01-22T10:34:18Z",
    "title_canon_sha256": "7dce01cb68b893e11cebab2f80e36d1cd8ad0d7bfe10bfeda064badfe24a94d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.09044",
    "kind": "arxiv",
    "version": 2
  }
}