Pith Number

pith:VWE64HRQ

pith:2026:VWE64HRQVKQ3JSBTCGGWFDV3AT

not attested not anchored not stored refs pending

Learning Bidirectional Causal Interactions with Heteroscedastic Neural Networks

Masahiro Tanaka

arxiv:2607.22313 v1 · 2026-07-24 · stat.ML · cs.LG · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VWE64HRQVKQ3JSBTCGGWFDV3AT}

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	2026-07-27T01:20:59.365124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad89ee1e30aaa1b4c833118d628ebb04ffd82acd9d40207b8d5b38c14a4eb6ac

Aliases

arxiv: 2607.22313 · arxiv_version: 2607.22313v1 · doi: 10.48550/arxiv.2607.22313 · pith_short_12: VWE64HRQVKQ3 · pith_short_16: VWE64HRQVKQ3JSBT · pith_short_8: VWE64HRQ

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/VWE64HRQVKQ3JSBTCGGWFDV3AT \
  | 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: ad89ee1e30aaa1b4c833118d628ebb04ffd82acd9d40207b8d5b38c14a4eb6ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f4cbbb1b7b59702947b59e384738dcf535cdb1c5a8a867c7ff28cb218bd3479",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ME"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-24T13:53:58Z",
    "title_canon_sha256": "fdba810da70f7c0e8097650ea66b7d42203cb9ef5305e0a9b7bb1230ebe4e0b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22313",
    "kind": "arxiv",
    "version": 1
  }
}