Pith Number

pith:VAJM6Q3O

pith:2015:VAJM6Q3OG64ZGMVC35KAVQ4LE5

not attested not anchored not stored refs pending

Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with $S^1$-action

Chin-Yu Hsiao, Xiaoshan Li

arxiv:1506.06459 v2 · 2015-06-22 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAJM6Q3OG64ZGMVC35KAVQ4LE5}

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	2026-05-18T00:13:38.301725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a812cf436e37b99332a2df540ac38b27479991733c0e22f5cfc6637b7d66ed29

Aliases

arxiv: 1506.06459 · arxiv_version: 1506.06459v2 · doi: 10.48550/arxiv.1506.06459 · pith_short_12: VAJM6Q3OG64Z · pith_short_16: VAJM6Q3OG64ZGMVC · pith_short_8: VAJM6Q3O

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/VAJM6Q3OG64ZGMVC35KAVQ4LE5 \
  | 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: a812cf436e37b99332a2df540ac38b27479991733c0e22f5cfc6637b7d66ed29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68536c0fca39bbe8eaf69aa493e30480fc33ba1b0355ffd42184f565e56d429a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2015-06-22T04:01:30Z",
    "title_canon_sha256": "5f6d9de9a07c187e186b926de246cd0a34b0f1e8f33306d4665ae4f1c5478599"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.06459",
    "kind": "arxiv",
    "version": 2
  }
}