Pith Number

pith:NUPKBHEL

pith:2019:NUPKBHEL3Q5FMGR5KMO3KYWWOG

not attested not anchored not stored refs pending

Smoothness and norm attainment of bounded bilinear operators between Banach spaces

Debmalya Sain

arxiv:1907.01955 v1 · 2019-07-03 · 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{NUPKBHEL3Q5FMGR5KMO3KYWWOG}

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	2026-05-17T23:41:34.383070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d1ea09c8bdc3a561a3d531db562d671920fddf9d43d965b95aaf1ec044b2b86

Aliases

arxiv: 1907.01955 · arxiv_version: 1907.01955v1 · doi: 10.48550/arxiv.1907.01955 · pith_short_12: NUPKBHEL3Q5F · pith_short_16: NUPKBHEL3Q5FMGR5 · pith_short_8: NUPKBHEL

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/NUPKBHEL3Q5FMGR5KMO3KYWWOG \
  | 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: 6d1ea09c8bdc3a561a3d531db562d671920fddf9d43d965b95aaf1ec044b2b86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0522a3a0bd67a9f46961dd5d3881f080c12f4bd36dbdc483411e2257bda16d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-07-03T14:11:09Z",
    "title_canon_sha256": "217cd999db467a534b3478d2439a7e7d7a2845cc493b95d275d076df2faa74e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.01955",
    "kind": "arxiv",
    "version": 1
  }
}