Pith Number

pith:MON2NTW6

pith:2026:MON2NTW6A4WDNUGNCAV4X5OKAM

not attested not anchored not stored refs pending

Operator Learning on the Data-Driven Multiscale Space for Nonlinear Flow in Random Heterogeneous Porous Media

Maria Vasilyeva, Raphael Pangilinan

arxiv:2606.25820 v1 · 2026-06-24 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MON2NTW6A4WDNUGNCAV4X5OKAM}

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	2026-06-25T01:18:40.347912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

639ba6cede072c36d0cd102bcbf5ca03128af6e552e277de7e448d957dd5629c

Aliases

arxiv: 2606.25820 · arxiv_version: 2606.25820v1 · doi: 10.48550/arxiv.2606.25820 · pith_short_12: MON2NTW6A4WD · pith_short_16: MON2NTW6A4WDNUGN · pith_short_8: MON2NTW6

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/MON2NTW6A4WDNUGNCAV4X5OKAM \
  | 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: 639ba6cede072c36d0cd102bcbf5ca03128af6e552e277de7e448d957dd5629c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91ebed4e4ac3e9c9ef33ce0fab554d8afd29d0ede9ab9a5de245f826e90a0c6c",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-24T13:36:31Z",
    "title_canon_sha256": "a628c44312170f132003371fb62555ecea5acf33d536536ff871fa117997d311"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25820",
    "kind": "arxiv",
    "version": 1
  }
}