Pith Number

pith:E66CHXZC

pith:2009:E66CHXZCX2NJU4MWCJRZIEQSUT

not attested not anchored not stored refs pending

The Pullbacks of Principal Coactions

Elmar Wagner, Piotr M. Hajac

arxiv:1001.0075 v3 · 2009-12-31 · math.KT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E66CHXZCX2NJU4MWCJRZIEQSUT}

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	2026-05-18T03:32:45.823009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27bc23df22be9a9a71961263941212a4db5685af61691591c205fb4cccaa5bfb

Aliases

arxiv: 1001.0075 · arxiv_version: 1001.0075v3 · doi: 10.48550/arxiv.1001.0075 · pith_short_12: E66CHXZCX2NJ · pith_short_16: E66CHXZCX2NJU4MW · pith_short_8: E66CHXZC

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/E66CHXZCX2NJU4MWCJRZIEQSUT \
  | 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: 27bc23df22be9a9a71961263941212a4db5685af61691591c205fb4cccaa5bfb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec45aae609f22fa639553556fc8083a85c3113b7a7812f15f1e6edd58906cf51",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2009-12-31T03:22:13Z",
    "title_canon_sha256": "f6d5fba243f57ab1b7b40ea3321535bd957455bdde936a1dd947d9e7b69bf6ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0075",
    "kind": "arxiv",
    "version": 3
  }
}