Pith Number

pith:64QMCNAV

pith:2009:64QMCNAVC6VSBXMG67VC4B65PA

not attested not anchored not stored refs pending

A short proof of the H\"older-Poincar\'{e} Duality for $L_{p}$-cohomology

Marc Troyanov, Vladimir Gol'dshtein

arxiv:0911.0998 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{64QMCNAVC6VSBXMG67VC4B65PA}

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	2026-05-18T03:40:37.034004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f720c1341517ab20dd86f7ea2e07dd782c14644e23faa88afdbdb59bd342761d

Aliases

arxiv: 0911.0998 · arxiv_version: 0911.0998v1 · doi: 10.48550/arxiv.0911.0998 · pith_short_12: 64QMCNAVC6VS · pith_short_16: 64QMCNAVC6VSBXMG · pith_short_8: 64QMCNAV

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/64QMCNAVC6VSBXMG67VC4B65PA \
  | 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: f720c1341517ab20dd86f7ea2e07dd782c14644e23faa88afdbdb59bd342761d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "259ce624d0a6b44fba7e00cdaf3009d63813a28777da76f48e8c71a68c7ea7e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-11-05T15:25:59Z",
    "title_canon_sha256": "fa232e27a1160da02faa216362a89923e0207cdb45b910cb1145a2dbdda0e8fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.0998",
    "kind": "arxiv",
    "version": 1
  }
}