Pith Number

pith:PD25NNY5

pith:2026:PD25NNY534AR5CVPRCDBI4EJVF

not attested not anchored not stored refs pending

Banach lattices and phase retrieval: A case study for the use of AI in mathematics

David Mu\~noz-Lahoz, Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor, Pedro Tradacete

arxiv:2608.07396 v1 · 2026-08-07 · 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{PD25NNY534AR5CVPRCDBI4EJVF}

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	2026-08-10T01:15:15.393474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78f5d6b71ddf011e8aaf8886147089a96c64f9e003b81946e53e334f1d0d3f11

Aliases

arxiv: 2608.07396 · arxiv_version: 2608.07396v1 · doi: 10.48550/arxiv.2608.07396 · pith_short_12: PD25NNY534AR · pith_short_16: PD25NNY534AR5CVP · pith_short_8: PD25NNY5

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/PD25NNY534AR5CVPRCDBI4EJVF \
  | 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: 78f5d6b71ddf011e8aaf8886147089a96c64f9e003b81946e53e334f1d0d3f11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "431a2f16173f3b713941d103d61625e9fc592ce16476b92533ec6a5dd136993c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-07T16:40:37Z",
    "title_canon_sha256": "d24a25aa9643e14ff52f97a0febdf51204db71b0d4d91311e0356db0ab38a213"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07396",
    "kind": "arxiv",
    "version": 1
  }
}