Pith Number

pith:DLLT5I5R

pith:2026:DLLT5I5RU7LJYDY7I6YA7REV6M

not attested not anchored not stored refs pending

Optimal minimax formula for bounds on ensemble averages of statistically stationary three-dimensional Navier-Stokes flows

Anne Bronzi, Cec\'ilia F. Mondaini, Ricardo M. S. Rosa

arxiv:2606.12825 v1 · 2026-06-11 · math.AP · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DLLT5I5RU7LJYDY7I6YA7REV6M}

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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	2026-06-12T01:08:52.931889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ad73ea3b1a7d69c0f1f47b00fc495f3215a922e63b9a2a3d0599dd6d9f07b22

Aliases

arxiv: 2606.12825 · arxiv_version: 2606.12825v1 · doi: 10.48550/arxiv.2606.12825 · pith_short_12: DLLT5I5RU7LJ · pith_short_16: DLLT5I5RU7LJYDY7 · pith_short_8: DLLT5I5R

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/DLLT5I5RU7LJYDY7I6YA7REV6M \
  | 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: 1ad73ea3b1a7d69c0f1f47b00fc495f3215a922e63b9a2a3d0599dd6d9f07b22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8a3818730cd5ec36390b3341f8b6ea15e1234c98c5b55c7ec32de7154f92301",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-11T02:43:42Z",
    "title_canon_sha256": "f9f2083e7840944c9806a501b721478481bffbbffc0c89193cf4f97054b0408f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12825",
    "kind": "arxiv",
    "version": 1
  }
}