Pith Number

pith:FD2C4VVM

pith:2016:FD2C4VVM2YKIXOOUK3IZAQTBTF

not attested not anchored not stored refs pending

Localization C*-algebras and K-theoretic duality

Jianchao Wu, Marius Dadarlat, Rufus Willett

arxiv:1609.06690 v2 · 2016-09-21 · math.KT · 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{FD2C4VVM2YKIXOOUK3IZAQTBTF}

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	2026-05-17T23:57:36.879201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28f42e56acd6148bb9d456d190426199714e66d4bfa157418bf3c6d4fde9ff7b

Aliases

arxiv: 1609.06690 · arxiv_version: 1609.06690v2 · doi: 10.48550/arxiv.1609.06690 · pith_short_12: FD2C4VVM2YKI · pith_short_16: FD2C4VVM2YKIXOOU · pith_short_8: FD2C4VVM

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/FD2C4VVM2YKIXOOUK3IZAQTBTF \
  | 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: 28f42e56acd6148bb9d456d190426199714e66d4bfa157418bf3c6d4fde9ff7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "449a7442538eaf64e49793c9d690e3649be5849f5f5556488161cec2e1abdf1d",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2016-09-21T19:12:56Z",
    "title_canon_sha256": "d8efa25c899b9b9d755cfce7c9d0cdecbc6d431cc1a6b0fe4c63ca3ca3a72bfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06690",
    "kind": "arxiv",
    "version": 2
  }
}