Pith Number

pith:RRVGTSME

pith:2011:RRVGTSMEU7MDCXZ6SN6255KUMM

not attested not anchored not stored refs pending

The localized longitudinal index theorem for Lie groupoids and the van Est map

H. Posthuma, M. J. Pflaum, X. Tang

arxiv:1112.4857 v1 · 2011-12-20 · math.KT · math.DG · 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{RRVGTSMEU7MDCXZ6SN6255KUMM}

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	2026-05-18T04:05:57.049119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c6a69c984a7d8315f3e937daef55463224e09a272c115fc8d46407d9cc2ed23

Aliases

arxiv: 1112.4857 · arxiv_version: 1112.4857v1 · doi: 10.48550/arxiv.1112.4857 · pith_short_12: RRVGTSMEU7MD · pith_short_16: RRVGTSMEU7MDCXZ6 · pith_short_8: RRVGTSME

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/RRVGTSMEU7MDCXZ6SN6255KUMM \
  | 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: 8c6a69c984a7d8315f3e937daef55463224e09a272c115fc8d46407d9cc2ed23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a60509e16f5eea1ded1889c7764050a81a271b8d35d5b3104c94858bb502d3fe",
    "cross_cats_sorted": [
      "math.DG",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2011-12-20T21:16:53Z",
    "title_canon_sha256": "fd3a2aaf7271d8a789607a35c6d1128ccfceb7bf3dcc75fc63c8b426a03d50a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4857",
    "kind": "arxiv",
    "version": 1
  }
}