Pith Number

pith:H2KPOMCR

pith:2012:H2KPOMCRW7WYYBRGEUVTM3MZEK

not attested not anchored not stored refs pending

Vanishing of $\ell^p$-cohomology and transportation cost

Antoine Gournay

arxiv:1207.0451 v7 · 2012-07-02 · math.GR · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H2KPOMCRW7WYYBRGEUVTM3MZEK}

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	2026-05-18T03:28:17.472146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e94f73051b7ed8c0626252b366d992292cd8f006169547fde1120b385070936

Aliases

arxiv: 1207.0451 · arxiv_version: 1207.0451v7 · doi: 10.48550/arxiv.1207.0451 · pith_short_12: H2KPOMCRW7WY · pith_short_16: H2KPOMCRW7WYYBRG · pith_short_8: H2KPOMCR

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/H2KPOMCRW7WYYBRGEUVTM3MZEK \
  | 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: 3e94f73051b7ed8c0626252b366d992292cd8f006169547fde1120b385070936

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccbf863cfd66f930594f5c8ccf36f9561b85a8366914c8889d14bd51612d5c73",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-02T17:44:34Z",
    "title_canon_sha256": "2db88882bdfe9b6632838ad1626f86cfec2dd6e1227300a05c9e6644c3276dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0451",
    "kind": "arxiv",
    "version": 7
  }
}