Pith Number

pith:JSECJTZ6

pith:2011:JSECJTZ63UV5N6DDCJMXO2HQML

not attested not anchored not stored refs pending

A geometric form of the Hahn-Banach extension theorem for L0 linear functions and the Goldstine-Weston theorem in random normed modules

Guang Shi, Shien Zhao

arxiv:1103.5318 v2 · 2011-03-28 · 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{JSECJTZ63UV5N6DDCJMXO2HQML}

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	2026-05-18T04:25:37.513860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c8824cf3edd2bd6f86312597768f062d2a9cc2fb85bf050d800e9ca3278c3c0

Aliases

arxiv: 1103.5318 · arxiv_version: 1103.5318v2 · doi: 10.48550/arxiv.1103.5318 · pith_short_12: JSECJTZ63UV5 · pith_short_16: JSECJTZ63UV5N6DD · pith_short_8: JSECJTZ6

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/JSECJTZ63UV5N6DDCJMXO2HQML \
  | 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: 4c8824cf3edd2bd6f86312597768f062d2a9cc2fb85bf050d800e9ca3278c3c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46fd69dc56fc80f6ea2faf20ab60c24d73b4c36bb9ac31f6797437c6a2800837",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-03-28T10:19:32Z",
    "title_canon_sha256": "d614953c11a5649eff5d609a093b6f42eed7228b17af7a05a45c77eba1ee5fa6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5318",
    "kind": "arxiv",
    "version": 2
  }
}