Pith Number

pith:KP7ZH6UR

pith:2026:KP7ZH6URZG52HICGOLAN74I3N5

not attested not anchored not stored refs pending

Lifted Schr\"odinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions

George Rapakoulias, Panagiotis Tsiotras, Siddhartha Ganguly

arxiv:2605.24795 v1 · 2026-05-24 · math.OC · cs.LG · cs.RO · cs.SY · eess.SY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KP7ZH6URZG52HICGOLAN74I3N5}

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	2026-05-26T01:03:58.781436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53ff93fa91c9bba3a04672c0dff11b6f48761b747babf2f6a6bc694e86c7bedd

Aliases

arxiv: 2605.24795 · arxiv_version: 2605.24795v1 · doi: 10.48550/arxiv.2605.24795 · pith_short_12: KP7ZH6URZG52 · pith_short_16: KP7ZH6URZG52HICG · pith_short_8: KP7ZH6UR

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/KP7ZH6URZG52HICGOLAN74I3N5 \
  | 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: 53ff93fa91c9bba3a04672c0dff11b6f48761b747babf2f6a6bc694e86c7bedd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3f235161a1c7e45066c07e6fd4f9aa9069f690b650780fc737069773edcf44e",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.RO",
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-24T00:38:29Z",
    "title_canon_sha256": "fd255b3305ab6103398afa91ba94b3721c8073ae2ab2b93219c64a00267e401b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.24795",
    "kind": "arxiv",
    "version": 1
  }
}