Pith Number

pith:PBXRFEH3

pith:2025:PBXRFEH3MUZMMOTNCDY72TBLQ3

not attested not anchored not stored refs pending

Dirac spectral flow and Floer theory of hyperbolic three-manifolds

Francesco Lin, Michael Lipnowski

arxiv:2506.07238 v1 · 2025-06-08 · math.GT · math.DG · math.NT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PBXRFEH3MUZMMOTNCDY72TBLQ3}

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	2026-07-05T11:18:04.088724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

786f1290fb6532c63a6d10f1fd4c2b86cb65c74b9708accfb09bbd760a8e5dc8

Aliases

arxiv: 2506.07238 · arxiv_version: 2506.07238v1 · doi: 10.48550/arxiv.2506.07238 · pith_short_12: PBXRFEH3MUZM · pith_short_16: PBXRFEH3MUZMMOTN · pith_short_8: PBXRFEH3

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/PBXRFEH3MUZMMOTNCDY72TBLQ3 \
  | 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: 786f1290fb6532c63a6d10f1fd4c2b86cb65c74b9708accfb09bbd760a8e5dc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed06e818d0a07a3b7d8fbe302951abae5cd4acf1357028a854df2f5bf301af4e",
    "cross_cats_sorted": [
      "math.DG",
      "math.NT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-06-08T17:46:03Z",
    "title_canon_sha256": "0910db0c023354d8bae7fa9d0e1a4ee52bc004014c500c52d049a4a6ee7be429"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07238",
    "kind": "arxiv",
    "version": 1
  }
}