Pith Number

pith:BI473CDB

pith:2012:BI473CDB53FKCMITFZZ6Z7CQVH

not attested not anchored not stored refs pending

The splitting lemmas for nonsmooth functionals on Hilbert spaces I

Guangcun Lu

arxiv:1211.2127 v2 · 2012-11-06 · math.FA · math.AP · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BI473CDB53FKCMITFZZ6Z7CQVH}

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	2026-05-18T02:50:01.018721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a39fd8861eecaa131132e73ecfc50a9e95efe378c648d3176f11e53eb0ba4eb

Aliases

arxiv: 1211.2127 · arxiv_version: 1211.2127v2 · doi: 10.48550/arxiv.1211.2127 · pith_short_12: BI473CDB53FK · pith_short_16: BI473CDB53FKCMIT · pith_short_8: BI473CDB

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/BI473CDB53FKCMITFZZ6Z7CQVH \
  | 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: 0a39fd8861eecaa131132e73ecfc50a9e95efe378c648d3176f11e53eb0ba4eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0972f6032b382eb0c90639e1aeaa6da11f0ecc0ccad1046ca4daefb63bf23c76",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-11-06T12:26:17Z",
    "title_canon_sha256": "ff66db433a8dd006d8aa611e6a40858ef6734a6b6bd1c035b6c55e1f87f89645"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2127",
    "kind": "arxiv",
    "version": 2
  }
}