Pith Number

pith:AQCWUDLJ

pith:2016:AQCWUDLJIYHWPFOLMZF3Z6TVQ6

not attested not anchored not stored refs pending

The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions

Pengshuai Shi

arxiv:1610.08141 v3 · 2016-10-26 · 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{AQCWUDLJIYHWPFOLMZF3Z6TVQ6}

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	2026-05-18T00:35:05.102705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04056a0d69460f6795cb664bbcfa758785626ccce4e0065add08175c6547ef87

Aliases

arxiv: 1610.08141 · arxiv_version: 1610.08141v3 · doi: 10.48550/arxiv.1610.08141 · pith_short_12: AQCWUDLJIYHW · pith_short_16: AQCWUDLJIYHWPFOL · pith_short_8: AQCWUDLJ

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/AQCWUDLJIYHWPFOLMZF3Z6TVQ6 \
  | 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: 04056a0d69460f6795cb664bbcfa758785626ccce4e0065add08175c6547ef87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8febcb5ba717d0e7a6e976796caaf60371b340d769c88664f3df410b4cbdbd2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-10-26T01:42:01Z",
    "title_canon_sha256": "3b322434071a58a0caf24318ea4ea6896fafa1569e0f9919ccae08e7575d97a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.08141",
    "kind": "arxiv",
    "version": 3
  }
}