Pith Number

pith:DXKRWR3U

pith:2009:DXKRWR3UK6SJOUEMO3I4POAKLA

not attested not anchored not stored refs pending

An index theorem of Callias type for pseudodifferential operators

Chris Kottke

arxiv:0909.5661 v2 · 2009-09-30 · math.KT · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DXKRWR3UK6SJOUEMO3I4POAKLA}

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	2026-05-18T03:43:53.138564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dd51b477457a497508c76d1c7b80a580cafd8798ff651ae9f25d8eb73dd2aaf

Aliases

arxiv: 0909.5661 · arxiv_version: 0909.5661v2 · doi: 10.48550/arxiv.0909.5661 · pith_short_12: DXKRWR3UK6SJ · pith_short_16: DXKRWR3UK6SJOUEM · pith_short_8: DXKRWR3U

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/DXKRWR3UK6SJOUEMO3I4POAKLA \
  | 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: 1dd51b477457a497508c76d1c7b80a580cafd8798ff651ae9f25d8eb73dd2aaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "688b774e3cb3cca026f206dde4b9a028fa88895240bb3c44474748d7b423d40b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2009-09-30T17:00:01Z",
    "title_canon_sha256": "eef9007ad067a4bb6bf2fb3e245bedb90d707add1dddfda40b153438f1dd0aad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.5661",
    "kind": "arxiv",
    "version": 2
  }
}