Pith Number

pith:DYJBVCOX

pith:2000:DYJBVCOX3TKZNYSY3HJUTBHU3C

not attested not anchored not stored refs pending

The eta-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary

Matthias Lesch, Paul Kirk

arxiv:math/0012123 v2 · 2000-12-15 · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DYJBVCOX3TKZNYSY3HJUTBHU3C}

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.

Cited by

2 papers in Pith

Second-Jet Equivariant $\eta$ Separations on Lens Spaces

Higher-Rank Orthogonal Twists, APS Boundary Conditions, and $O(2)$-Equivariant Spectral Flow on a Warped Cylinder

Receipt and verification

First computed	2026-07-04T14:47:58.553921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e121a89d7dcd596e258d9d34984f4d8a546b672af5806a93ffb9ab95ccb97c4

Aliases

arxiv: math/0012123 · arxiv_version: math/0012123v2 · doi: 10.48550/arxiv.math/0012123 · pith_short_12: DYJBVCOX3TKZ · pith_short_16: DYJBVCOX3TKZNYSY · pith_short_8: DYJBVCOX

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/DYJBVCOX3TKZNYSY3HJUTBHU3C \
  | 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: 1e121a89d7dcd596e258d9d34984f4d8a546b672af5806a93ffb9ab95ccb97c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d023dff571a170b7cf22d28bce3a6ec321523b584f25ff26ca6cf41710ef7ab3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2000-12-15T17:13:57Z",
    "title_canon_sha256": "802ae43145029354daff1d0627170e47ef95ffe974c6b10d1f4a44c5344cce31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012123",
    "kind": "arxiv",
    "version": 2
  }
}