Pith Number

pith:L5QPZHJD

pith:2026:L5QPZHJDLHZLGQLK2AR6XDVROX

not attested not anchored not stored refs pending

Irreducible proper 2-knots from exotic open 2-handles

Sean Eli

arxiv:2607.19481 v1 · 2026-07-21 · math.GT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5QPZHJDLHZLGQLK2AR6XDVROX}

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	2026-07-23T00:23:52.049513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f60fc9d2359f2b3416ad023eb8eb175d822d15b2d4c9c16bfdae67a5af89162

Aliases

arxiv: 2607.19481 · arxiv_version: 2607.19481v1 · doi: 10.48550/arxiv.2607.19481 · pith_short_12: L5QPZHJDLHZL · pith_short_16: L5QPZHJDLHZLGQLK · pith_short_8: L5QPZHJD

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/L5QPZHJDLHZLGQLK2AR6XDVROX \
  | 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: 5f60fc9d2359f2b3416ad023eb8eb175d822d15b2d4c9c16bfdae67a5af89162

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc3d02a10e7493962ebfbcaba21d31b8570b620eb89e23ddb642bf147eba9a3b",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-21T18:02:35Z",
    "title_canon_sha256": "458d5b6bdc1fa97f915c6a7f0b4f3349e87a7c87b186a0e9f11cd55d65dc3ea8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19481",
    "kind": "arxiv",
    "version": 1
  }
}