Pith Number

pith:LHV7BB5M

pith:2018:LHV7BB5MJT362UX6WAZW3RPNM5

not attested not anchored not stored refs pending

Brezis - Lieb spaces and an operator version of Brezis - Lieb's lemma

Eduard Emelyanov, Mohammad Marabeh

arxiv:1805.09548 v2 · 2018-05-24 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LHV7BB5MJT362UX6WAZW3RPNM5}

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	2026-05-18T00:14:13.511122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59ebf087ac4cf7ed52feb0336dc5ed6740be289a0e318655bd38e65c96c30935

Aliases

arxiv: 1805.09548 · arxiv_version: 1805.09548v2 · doi: 10.48550/arxiv.1805.09548 · pith_short_12: LHV7BB5MJT36 · pith_short_16: LHV7BB5MJT362UX6 · pith_short_8: LHV7BB5M

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/LHV7BB5MJT362UX6WAZW3RPNM5 \
  | 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: 59ebf087ac4cf7ed52feb0336dc5ed6740be289a0e318655bd38e65c96c30935

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66a28cb70d44fde004107d393de798e45152a6248fb933228f960de1f3e854b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-05-24T08:33:03Z",
    "title_canon_sha256": "c418ea035b35ea53bbce8d8a82144a56924fa21fb4f49d0acdf38a3e6f782512"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.09548",
    "kind": "arxiv",
    "version": 2
  }
}