Pith Number

pith:HLWV7QO6

pith:2011:HLWV7QO6DTZROJXU6MXN7UWIPT

not attested not anchored not stored refs pending

The multiplicative property characterizes $\ell_p$ and $L_p$ norms

Guillaume Aubrun, Ion Nechita

arxiv:1102.2618 v1 · 2011-02-13 · 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{HLWV7QO6DTZROJXU6MXN7UWIPT}

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.

Cited by

2 papers in Pith

Quantitative Linear Logic for Neuro-Symbolic Learning and Verification

Receipt and verification

First computed	2026-05-18T03:41:21.596249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aed5fc1de1cf31726f4f32edfd2c87ccded7594d0060b1cbc0e860fc292fd0f

Aliases

arxiv: 1102.2618 · arxiv_version: 1102.2618v1 · doi: 10.48550/arxiv.1102.2618 · pith_short_12: HLWV7QO6DTZR · pith_short_16: HLWV7QO6DTZROJXU · pith_short_8: HLWV7QO6

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/HLWV7QO6DTZROJXU6MXN7UWIPT \
  | 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: 3aed5fc1de1cf31726f4f32edfd2c87ccded7594d0060b1cbc0e860fc292fd0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a6c9221dc8577aac7d0f839a20d53254fc6b5cf0e9b6372964b4456933e68af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-02-13T17:16:53Z",
    "title_canon_sha256": "88d82aa0e36bb87b3a9023b0f274a15bc324e2586840f59fabe0093defa20902"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2618",
    "kind": "arxiv",
    "version": 1
  }
}