Pith Number

pith:MJWDM4UI

pith:2026:MJWDM4UIJ6FHGPTLAZVFTLN2PP

not attested not anchored not stored refs pending

$E$-theory of $X$-$C^{*}$-algebras and functor formalisms

Ulrich Bunke

arxiv:2605.19863 v1 · 2026-05-19 · math.KT · math.AT · 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{MJWDM4UIJ6FHGPTLAZVFTLN2PP}

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	2026-05-20T01:06:18.126705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

626c3672884f8a733e6b066a59adba7be0f291157a62b54d3d0fcc8adcd0106e

Aliases

arxiv: 2605.19863 · arxiv_version: 2605.19863v1 · doi: 10.48550/arxiv.2605.19863 · pith_short_12: MJWDM4UIJ6FH · pith_short_16: MJWDM4UIJ6FHGPTL · pith_short_8: MJWDM4UI

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/MJWDM4UIJ6FHGPTLAZVFTLN2PP \
  | 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: 626c3672884f8a733e6b066a59adba7be0f291157a62b54d3d0fcc8adcd0106e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43a7b3bbbd37769c7afa883c266e1f447142a5a196df2372c7b75a524f0ddbef",
    "cross_cats_sorted": [
      "math.AT",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2026-05-19T13:55:29Z",
    "title_canon_sha256": "f68ca64f36467a1986bb9fd9d147c079c0ebf56520139468f2579839e521c13a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19863",
    "kind": "arxiv",
    "version": 1
  }
}