Pith Number

pith:Z2NGXKHE

pith:2009:Z2NGXKHE3RDITEWX43VONPGKW5

not attested not anchored not stored refs pending

The H\"older-Poincar\'e Duality for $L_{q,p}$-cohomology

Marc Troyanov, Vladimir Gol'dshtein

arxiv:0911.1059 v1 · 2009-11-05 · 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{Z2NGXKHE3RDITEWX43VONPGKW5}

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	2026-05-18T03:40:37.023005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce9a6ba8e4dc468992d7e6eae6bccab76d05f1d06d09920c0502621634dc6fc4

Aliases

arxiv: 0911.1059 · arxiv_version: 0911.1059v1 · doi: 10.48550/arxiv.0911.1059 · pith_short_12: Z2NGXKHE3RDI · pith_short_16: Z2NGXKHE3RDITEWX · pith_short_8: Z2NGXKHE

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/Z2NGXKHE3RDITEWX43VONPGKW5 \
  | 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: ce9a6ba8e4dc468992d7e6eae6bccab76d05f1d06d09920c0502621634dc6fc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9de1b5e130ca11614727c426bc32d336ba1c19744e0ec807575d5d419d0b5df0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-11-05T15:33:27Z",
    "title_canon_sha256": "3d0292b4cad901792217e94793b54f54edefff9001053820670c5d7915a30449"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1059",
    "kind": "arxiv",
    "version": 1
  }
}