Pith Number

pith:ZGD4XOE7

pith:2026:ZGD4XOE7JXBXKKB3HZ65GZ76HT

not attested not anchored not stored refs resolved

Liquid Tree Automata

Ashish Mishra, Suresh Jagannathan

Liquid Tree Automata merge semantically similar states using subtyping from refinement types to speed up component-based synthesis.

arxiv:2605.13456 v1 · 2026-05-13 · cs.PL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZGD4XOE7JXBXKKB3HZ65GZ76HT}

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.

Claims

C1strongest claim

LTAs leverage subtyping constraints to identify and eagerly merge semantically similar states during search. This merging avoids redundant exploration of equivalent paths, significantly improving synthesis efficiency.

C2weakest assumption

That subtyping constraints derived from refinement types accurately capture semantic equivalence of exploration paths without either missing valid solutions or incorrectly merging distinct paths.

C3one line summary

Liquid Tree Automata merge similar states during synthesis search via refinement subtyping to avoid redundant exploration and handle complex queries more efficiently.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] Recursive Program Syn- thesis 2013

[2] Olausson, Lionel Wong, Gabriel Grand, Joshua B 2023

[3] Babble: Learning Better Abstractions with E-Graphs and Anti- Unification 2023

[4] VOCAL – A Verified OCaml Library 2017

[5] Tree Automata Techniques and Applications 1997

Receipt and verification

First computed	2026-05-18T02:44:41.801967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c987cbb89f4dc375283b3e7dd367fe3cc1c0ff64bc0c1fdf3f572d57b0fe9d77

Aliases

arxiv: 2605.13456 · arxiv_version: 2605.13456v1 · doi: 10.48550/arxiv.2605.13456 · pith_short_12: ZGD4XOE7JXBX · pith_short_16: ZGD4XOE7JXBXKKB3 · pith_short_8: ZGD4XOE7

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/ZGD4XOE7JXBXKKB3HZ65GZ76HT \
  | 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: c987cbb89f4dc375283b3e7dd367fe3cc1c0ff64bc0c1fdf3f572d57b0fe9d77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a08bd09589793e59e7b014b6aefa79868d5fa71ee0023384c9d482a6a59e08a1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.PL",
    "submitted_at": "2026-05-13T12:49:32Z",
    "title_canon_sha256": "ee67eeb12014e7798d56356b3f7e0621a205025f5442f9d0a56ce429201ccae4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13456",
    "kind": "arxiv",
    "version": 1
  }
}