Pith Number

pith:LB2DWZBZ

pith:2012:LB2DWZBZCAUU56X7Y45AHM4TA2

not attested not anchored not stored refs pending

Homology of saddle point reduction and applications to resonant elliptic systems

Chong Li, Shibo Liu

arxiv:1208.5312 v1 · 2012-08-27 · math.AP · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LB2DWZBZCAUU56X7Y45AHM4TA2}

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	2026-05-18T03:46:59.811867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58743b643910294efaffc73a03b393068bedc866f1c05c1f3db3d3c7d02d74d9

Aliases

arxiv: 1208.5312 · arxiv_version: 1208.5312v1 · doi: 10.48550/arxiv.1208.5312 · pith_short_12: LB2DWZBZCAUU · pith_short_16: LB2DWZBZCAUU56X7 · pith_short_8: LB2DWZBZ

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/LB2DWZBZCAUU56X7Y45AHM4TA2 \
  | 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: 58743b643910294efaffc73a03b393068bedc866f1c05c1f3db3d3c7d02d74d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4046411c62389378082215386f0d368331d0aa5a1dee7fc6968678b8af9e32e",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-27T07:26:58Z",
    "title_canon_sha256": "cc8e115c70dbcd8e430e446a4290dd4a4f5a7fb392f3edf1a5233184329e118a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5312",
    "kind": "arxiv",
    "version": 1
  }
}