Pith Number

pith:S53VC42J

pith:2016:S53VC42JQHLMIY7DDSO54LCRZC

not attested not anchored not stored refs pending

Group Riesz and Frame Sequences: The Bracket and the Gramian

Davide Barbieri, Eugenio Hernandez, Victoria Paternostro

arxiv:1608.02767 v1 · 2016-08-09 · 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{S53VC42JQHLMIY7DDSO54LCRZC}

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	2026-05-18T01:09:33.713279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

977751734981d6c463e31c9dde2c51c888f8a08237d9aa326b105049a7686e42

Aliases

arxiv: 1608.02767 · arxiv_version: 1608.02767v1 · doi: 10.48550/arxiv.1608.02767 · pith_short_12: S53VC42JQHLM · pith_short_16: S53VC42JQHLMIY7D · pith_short_8: S53VC42J

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/S53VC42JQHLMIY7DDSO54LCRZC \
  | 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: 977751734981d6c463e31c9dde2c51c888f8a08237d9aa326b105049a7686e42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c2cc95939fb47125f01842c916a24ce44ead4f37005404f91062dcbdcfcf9bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-08-09T11:36:43Z",
    "title_canon_sha256": "7d6514394ba024c4ab29116f4aaf11841f249ef4d091a0cf26514b165b8a28f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02767",
    "kind": "arxiv",
    "version": 1
  }
}