Pith Number

pith:VVHN4AKL

pith:2016:VVHN4AKLAYJE3WZWDSWBPO6UX7

not attested not anchored not stored refs pending

A direct proof of F. Riesz representation Theorem

Asaf Franco, Jose Lara, Rafael del Rio

arxiv:1606.05026 v2 · 2016-06-16 · 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{VVHN4AKLAYJE3WZWDSWBPO6UX7}

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	2026-05-18T00:40:51.694603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad4ede014b06124ddb361cac17bbd4bfc8acfd80a0937c4e0851f3cd47ca539e

Aliases

arxiv: 1606.05026 · arxiv_version: 1606.05026v2 · doi: 10.48550/arxiv.1606.05026 · pith_short_12: VVHN4AKLAYJE · pith_short_16: VVHN4AKLAYJE3WZW · pith_short_8: VVHN4AKL

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/VVHN4AKLAYJE3WZWDSWBPO6UX7 \
  | 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: ad4ede014b06124ddb361cac17bbd4bfc8acfd80a0937c4e0851f3cd47ca539e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52b2244399594c956b814cfc4de8cfd2bdea3399cf9d2c828707e7fb5dd0537c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-06-16T01:52:39Z",
    "title_canon_sha256": "86d52af20f1c5296c2542437031bae721d0d375fe8d40a0a6fd1a26edb9c95b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05026",
    "kind": "arxiv",
    "version": 2
  }
}