Pith Number

pith:KH52CUTZ

pith:2017:KH52CUTZAF5GYQDSY5G6IX7SF6

not attested not anchored not stored refs pending

Relationships between cycle spaces, gain graphs, graph coverings, fundamental groups, path homology, and graph curvature

Florentin Munch, Mark Kempton, Shing-Tung Yau

arxiv:1710.01264 v2 · 2017-10-03 · 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{KH52CUTZAF5GYQDSY5G6IX7SF6}

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	2026-05-18T00:28:40.327984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51fba15279017a6c4072c74de45ff22fbfa88550f0f79dff459064a369c9ffbf

Aliases

arxiv: 1710.01264 · arxiv_version: 1710.01264v2 · doi: 10.48550/arxiv.1710.01264 · pith_short_12: KH52CUTZAF5G · pith_short_16: KH52CUTZAF5GYQDS · pith_short_8: KH52CUTZ

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/KH52CUTZAF5GYQDSY5G6IX7SF6 \
  | 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: 51fba15279017a6c4072c74de45ff22fbfa88550f0f79dff459064a369c9ffbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94bd7515475e0763f4f768ada172f12205a6b7606a1a3facacad9a90864cbf28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-10-03T16:26:18Z",
    "title_canon_sha256": "968a7e6b477b902b64b5bbc82e9adbd7f00f216453b8b109ea68513d773e0df9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.01264",
    "kind": "arxiv",
    "version": 2
  }
}