Pith Number

pith:ZPYCGQO5

pith:2015:ZPYCGQO5JPR5W3TTH3MMVK55MK

not attested not anchored not stored refs pending

Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem

Mich\`ele Vergne (IMJ), Paul-Emile Paradan (IMAG)

arxiv:1504.07502 v2 · 2015-04-28 · math.SG · math.KT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZPYCGQO5JPR5W3TTH3MMVK55MK}

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	2026-05-18T01:23:12.347251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbf02341dd4be3db6e733ed8caabbd6298d70ebc24bcb0729835c0c1c6b2c422

Aliases

arxiv: 1504.07502 · arxiv_version: 1504.07502v2 · doi: 10.48550/arxiv.1504.07502 · pith_short_12: ZPYCGQO5JPR5 · pith_short_16: ZPYCGQO5JPR5W3TT · pith_short_8: ZPYCGQO5

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/ZPYCGQO5JPR5W3TTH3MMVK55MK \
  | 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: cbf02341dd4be3db6e733ed8caabbd6298d70ebc24bcb0729835c0c1c6b2c422

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3a23087820a291e991e05f83c25f0a82e51ad46396485424067a3371acfd150",
    "cross_cats_sorted": [
      "math.KT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-04-28T14:35:34Z",
    "title_canon_sha256": "c9d92cd40c4bf6805f06720875d586394bf46a133843300865c00c4a685ae452"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07502",
    "kind": "arxiv",
    "version": 2
  }
}