Pith Number

pith:2RGZUD33

pith:2026:2RGZUD334ABWDRB4RYTAG6BIUK

not attested not anchored not stored refs pending

Some closed manifolds that do not fibre over the circle

Ian Leary, Sam Hughes, Wolfgang Lueck

arxiv:2606.31254 v1 · 2026-06-30 · math.AT · 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{2RGZUD334ABWDRB4RYTAG6BIUK}

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	2026-07-01T01:17:57.237261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d44d9a0f7be00361c43c8e26037828a2b7868cc4ecd21420bca8d933452c4879

Aliases

arxiv: 2606.31254 · arxiv_version: 2606.31254v1 · doi: 10.48550/arxiv.2606.31254 · pith_short_12: 2RGZUD334ABW · pith_short_16: 2RGZUD334ABWDRB4 · pith_short_8: 2RGZUD33

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/2RGZUD334ABWDRB4RYTAG6BIUK \
  | 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: d44d9a0f7be00361c43c8e26037828a2b7868cc4ecd21420bca8d933452c4879

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d993ca267f409d14f4e95b6b89bdecf246f8820532613602c886afce29a066f2",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-30T07:31:27Z",
    "title_canon_sha256": "ac152ea7a1230d137dc3f35efd74ba51f587bd6287e9fbd007a639544ea2025b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31254",
    "kind": "arxiv",
    "version": 1
  }
}