Pith Number

pith:4BJ35OLW

pith:2015:4BJ35OLWENJH4FNZ32ITUKUE47

not attested not anchored not stored refs pending

Cobordism Invariance of the Index of Callias-Type Operators

Maxim Braverman, Pengshuai Shi

arxiv:1512.03939 v1 · 2015-12-12 · 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{4BJ35OLWENJH4FNZ32ITUKUE47}

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	2026-05-18T01:24:23.542288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e053beb97623527e15b9de913a2a84e7e09eda9c4889cba8f35c795c114dd781

Aliases

arxiv: 1512.03939 · arxiv_version: 1512.03939v1 · doi: 10.48550/arxiv.1512.03939 · pith_short_12: 4BJ35OLWENJH · pith_short_16: 4BJ35OLWENJH4FNZ · pith_short_8: 4BJ35OLW

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/4BJ35OLWENJH4FNZ32ITUKUE47 \
  | 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: e053beb97623527e15b9de913a2a84e7e09eda9c4889cba8f35c795c114dd781

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1efd22f677168820c9ab56b0af6c0c72fecb5ef6179fc95443850cc195a16e37",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-12-12T17:33:34Z",
    "title_canon_sha256": "fa9f8d6dca925127473a53c2840263c4de0432c61a0a91fb43b39c210a10415d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03939",
    "kind": "arxiv",
    "version": 1
  }
}