Pith Number

pith:X4243WSN

pith:2026:X4243WSNHCL7QQ6HZ5R2IOYMO5

not attested not anchored not stored refs pending

Chromatic Euler characteristics and duality for infinite groups

Gijs Heuts, Irakli Patchkoria

arxiv:2606.28107 v1 · 2026-06-26 · math.AT · math.GR · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X4243WSNHCL7QQ6HZ5R2IOYMO5}

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	2026-06-29T01:15:06.276506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf35cdda4d3897f843c7cf63a43b0c776f5e138f770e4fa79ef368f547be976c

Aliases

arxiv: 2606.28107 · arxiv_version: 2606.28107v1 · doi: 10.48550/arxiv.2606.28107 · pith_short_12: X4243WSNHCL7 · pith_short_16: X4243WSNHCL7QQ6H · pith_short_8: X4243WSN

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/X4243WSNHCL7QQ6HZ5R2IOYMO5 \
  | 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: bf35cdda4d3897f843c7cf63a43b0c776f5e138f770e4fa79ef368f547be976c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f54a8d792ad6c50dbf85dfb44f3ab1b2b26a115b30e812079471112a08902586",
    "cross_cats_sorted": [
      "math.GR",
      "math.KT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-26T14:07:17Z",
    "title_canon_sha256": "a753871912a96d3738409f1f975e68fc1cf56e9fd07027f865e8779dd4950133"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28107",
    "kind": "arxiv",
    "version": 1
  }
}