Pith Number

pith:ARL4VX6E

pith:2011:ARL4VX6EDUNIMUICF2LDHK3EM5

not attested not anchored not stored refs pending

Widths of embeddings in weighted function spaces

Gensun Fang, Shun Zhang

arxiv:1102.0681 v2 · 2011-02-03 · math.FA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ARL4VX6EDUNIMUICF2LDHK3EM5}

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	2026-05-18T01:49:56.372705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0457cadfc41d1a8651022e9633ab64677e41872b66bc0b4141ac830d39576c77

Aliases

arxiv: 1102.0681 · arxiv_version: 1102.0681v2 · doi: 10.48550/arxiv.1102.0681 · pith_short_12: ARL4VX6EDUNI · pith_short_16: ARL4VX6EDUNIMUIC · pith_short_8: ARL4VX6E

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/ARL4VX6EDUNIMUICF2LDHK3EM5 \
  | 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: 0457cadfc41d1a8651022e9633ab64677e41872b66bc0b4141ac830d39576c77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "073d66fd97f310bd0e1c5b9212849404b5e3c7df3bd5c16f28a3634cc1cf6846",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-02-03T13:35:57Z",
    "title_canon_sha256": "3d68356a11f675aee2a9cad8430aa49f9a05684918a2910512e0fa0a0c39ef2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0681",
    "kind": "arxiv",
    "version": 2
  }
}