Pith Number

pith:F3ZHV7TV

pith:2004:F3ZHV7TVMBA4NVUSBD7H6HUZ3D

not attested not anchored not stored refs pending

A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connections

Benjamin Himpel

arxiv:math/0412191 v3 · 2004-12-09 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F3ZHV7TVMBA4NVUSBD7H6HUZ3D}

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	2026-05-18T02:37:59.848653Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff

Aliases

arxiv: math/0412191 · arxiv_version: math/0412191v3 · doi: 10.48550/arxiv.math/0412191 · pith_short_12: F3ZHV7TVMBA4 · pith_short_16: F3ZHV7TVMBA4NVUS · pith_short_8: F3ZHV7TV

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/F3ZHV7TVMBA4NVUSBD7H6HUZ3D \
  | 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: 2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "449006e52448b031012c949aac790dbbc3e398b75f924ad2919c83e912744c88",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-12-09T16:14:12Z",
    "title_canon_sha256": "749809ab1adcf65f1e47b828d5c54db06d5f385c7ccb9a9f34214e4ca62a054f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412191",
    "kind": "arxiv",
    "version": 3
  }
}