Pith Number

pith:TZTODWTF

pith:2026:TZTODWTFX24LW5NI57VHUKJRCR

not attested not anchored not stored refs pending

Weak split extensions of topological Abelian groups

Luis Javier Hern\'andez-Paricio, Mar\'ia V. Ferrer, Salvador Hern\'andez-Mu\~noz

arxiv:2606.08069 v1 · 2026-06-06 · math.AT · math.CT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZTODWTFX24LW5NI57VHUKJRCR}

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	2026-06-09T01:05:25.291214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e66e1da65beb8bb75a8efea7a2931147bc3f382c132e6c6955aac54c2e53ba1

Aliases

arxiv: 2606.08069 · arxiv_version: 2606.08069v1 · doi: 10.48550/arxiv.2606.08069 · pith_short_12: TZTODWTFX24L · pith_short_16: TZTODWTFX24LW5NI · pith_short_8: TZTODWTF

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/TZTODWTFX24LW5NI57VHUKJRCR \
  | 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: 9e66e1da65beb8bb75a8efea7a2931147bc3f382c132e6c6955aac54c2e53ba1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36f11bee3f2092e7a179f257e8d711739a11e6abbc8d6aba9b45c2f23bd75233",
    "cross_cats_sorted": [
      "math.CT",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-06T09:34:08Z",
    "title_canon_sha256": "a233b1dc4cee1d97e76671bf614f30906bfbf81c0e7e21fdaaf3b5a4d3ddb3f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08069",
    "kind": "arxiv",
    "version": 1
  }
}