Pith Number

pith:M32AOFV4

pith:2026:M32AOFV4B2ETJB6Y5IJLRNKMBI

not attested not anchored not stored refs pending

Gauge-Invariant Learnable Spectral Positional Encodings for Directed Graphs via Hermitian Block Krylov Subspaces

Jiaqing Xie, Yuxin Wang

arxiv:2607.07032 v1 · 2026-07-08 · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M32AOFV4B2ETJB6Y5IJLRNKMBI}

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	2026-07-09T01:20:12.860327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66f40716bc0e893487d8ea12b8b54c0a16a57e10571f130d8381c4a9a6672970

Aliases

arxiv: 2607.07032 · arxiv_version: 2607.07032v1 · doi: 10.48550/arxiv.2607.07032 · pith_short_12: M32AOFV4B2ET · pith_short_16: M32AOFV4B2ETJB6Y · pith_short_8: M32AOFV4

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/M32AOFV4B2ETJB6Y5IJLRNKMBI \
  | 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: 66f40716bc0e893487d8ea12b8b54c0a16a57e10571f130d8381c4a9a6672970

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c0bbb9244adfdfbb6be3c2c7c648db97be33e3779f37b3792e940e8e1d5cab3",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-08T06:05:54Z",
    "title_canon_sha256": "59a6a0d4f5974b2b902ded16c276f0a44c25658748eb13d604b167a7cfc6c103"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07032",
    "kind": "arxiv",
    "version": 1
  }
}