Pith Number

pith:PBEDR4Q6

pith:2017:PBEDR4Q6BXATZLE4QEICK2D4L7

not attested not anchored not stored refs pending

A more symmetric picture for Kasparov's KK-bifunctor

Vladimir Manuilov

arxiv:1710.00330 v1 · 2017-10-01 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PBEDR4Q6BXATZLE4QEICK2D4L7}

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	2026-05-18T00:33:55.117854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

784838f21e0dc13cac9c811025687c5fec9ad022765b606b7faf5a5aa173ae36

Aliases

arxiv: 1710.00330 · arxiv_version: 1710.00330v1 · doi: 10.48550/arxiv.1710.00330 · pith_short_12: PBEDR4Q6BXAT · pith_short_16: PBEDR4Q6BXATZLE4 · pith_short_8: PBEDR4Q6

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/PBEDR4Q6BXATZLE4QEICK2D4L7 \
  | 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: 784838f21e0dc13cac9c811025687c5fec9ad022765b606b7faf5a5aa173ae36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d63244d69b2795f91b5301e7cc3d8fae917a1800ba3c6e3f3fe14e8fe2820e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-10-01T10:52:34Z",
    "title_canon_sha256": "0717f9e457e8b6d431a81603fc61c3cd38506d392f47b3b566fba861d06525ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.00330",
    "kind": "arxiv",
    "version": 1
  }
}