Pith Number

pith:7WA72YYL

pith:2013:7WA72YYLU5UARPCBILUZ7B77QB

not attested not anchored not stored refs pending

Sub-Hardy Hilbert spaces on the circle and torus

Ajay Kumar, Dinesh Singh, Niteesh Sahni

arxiv:1310.6619 v1 · 2013-10-24 · 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{7WA72YYLU5UARPCBILUZ7B77QB}

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	2026-05-18T03:09:08.846593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd81fd630ba76808bc4142e99f87ff806945229481934c5866a095380759dbf0

Aliases

arxiv: 1310.6619 · arxiv_version: 1310.6619v1 · doi: 10.48550/arxiv.1310.6619 · pith_short_12: 7WA72YYLU5UA · pith_short_16: 7WA72YYLU5UARPCB · pith_short_8: 7WA72YYL

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/7WA72YYLU5UARPCBILUZ7B77QB \
  | 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: fd81fd630ba76808bc4142e99f87ff806945229481934c5866a095380759dbf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c870ff08670855bff5474f03949b67d9e4354ab18827a69a64699cf4b326cbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-10-24T13:58:32Z",
    "title_canon_sha256": "bd7fbd04184978d05073ac54b156447b41c51eb1f5d047843095d6d04cdd3760"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6619",
    "kind": "arxiv",
    "version": 1
  }
}