Pith Number

pith:ILHMQ7QX

pith:2024:ILHMQ7QXN5JLNJCVPDNHY6LN6O

not attested not anchored not stored refs pending

Dual-Valued Functions of Dual Matrices with Applications in Causal Emergence

Tong Wei, Weiyang Ding, Yimin Wei

arxiv:2411.08377 v1 · 2024-11-13 · 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{ILHMQ7QXN5JLNJCVPDNHY6LN6O}

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	2026-07-05T09:34:46.404522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42cec87e176f52b6a45578da7c796df3931b99177789db15b98062a64efda13d

Aliases

arxiv: 2411.08377 · arxiv_version: 2411.08377v1 · doi: 10.48550/arxiv.2411.08377 · pith_short_12: ILHMQ7QXN5JL · pith_short_16: ILHMQ7QXN5JLNJCV · pith_short_8: ILHMQ7QX

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/ILHMQ7QXN5JLNJCVPDNHY6LN6O \
  | 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: 42cec87e176f52b6a45578da7c796df3931b99177789db15b98062a64efda13d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eae53907f6840e91926a8b943ca136ab30c3589f7524ee12cc1c623e22c40306",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-11-13T06:57:10Z",
    "title_canon_sha256": "b9e8d80bb41d8b594ca455b5a6d4c608969e56003033b88b82a02549c997c7be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.08377",
    "kind": "arxiv",
    "version": 1
  }
}