{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4PPOHL44E4LDOZW3WFSH3ADYVQ","short_pith_number":"pith:4PPOHL44","canonical_record":{"source":{"id":"2607.19126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T14:13:09Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"7897101965bbeb7f5693585ef96407a31ecedc78f6769da4d5b2a6d2607805e8","abstract_canon_sha256":"860f84d7083c303569709f9a255f5d52f4a3d9a014b07d87d65f70a27e8bf3cb"},"schema_version":"1.0"},"canonical_sha256":"e3dee3af9c27163766dbb1647d8078ac37b785d2208f6743fe1f6b4890546722","source":{"kind":"arxiv","id":"2607.19126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19126","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19126v1","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19126","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"4PPOHL44E4LD","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"pith_short_16","alias_value":"4PPOHL44E4LDOZW3","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"pith_short_8","alias_value":"4PPOHL44","created_at":"2026-07-22T01:24:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4PPOHL44E4LDOZW3WFSH3ADYVQ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.19126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T14:13:09Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"7897101965bbeb7f5693585ef96407a31ecedc78f6769da4d5b2a6d2607805e8","abstract_canon_sha256":"860f84d7083c303569709f9a255f5d52f4a3d9a014b07d87d65f70a27e8bf3cb"},"schema_version":"1.0"},"canonical_sha256":"e3dee3af9c27163766dbb1647d8078ac37b785d2208f6743fe1f6b4890546722","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:24:09.931603Z","signature_b64":"o1xG34MtuAEc6QKxmsNqz/IJ4nbNFHPA7WuRivrz+wNOZQdgj7EtCqLUFd4foyzz4trSBthc0EQ1NJ9ew4HyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3dee3af9c27163766dbb1647d8078ac37b785d2208f6743fe1f6b4890546722","last_reissued_at":"2026-07-22T01:24:09.930692Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:24:09.930692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.19126","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-22T01:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tvTwbQ+dMEdlgVTDkGFoUyUMTPDnQHFxY6zC6bSPzTc7bah3l7qW1QRviqGU3ovV7n4xhOJcVU8w2OB0j07BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:02:38.302038Z"},"content_sha256":"d423a145ee3ff13eaa2e2116b9cbb26c911c8fe804b5c4803e8343ad79202a93","schema_version":"1.0","event_id":"sha256:d423a145ee3ff13eaa2e2116b9cbb26c911c8fe804b5c4803e8343ad79202a93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4PPOHL44E4LDOZW3WFSH3ADYVQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel Noising in Neural Markov Logic Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Giuseppe Marra, Ondrej Kuzelka, Peter Jung","submitted_at":"2026-07-21T14:13:09Z","abstract_excerpt":"Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19126","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.19126/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-22T01:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"newUCb/qRJ4mSYyUGPME2va3ZidUzFBH+UJ/pDgPi0forymGqmVUBV0FmIiTin5FyfIgn+1/TZekz9RpISapCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:02:38.302561Z"},"content_sha256":"b2f3af7a7d4a6b71fb07a9d9a6f560c95cedfb94ac682e6f4300cf131453913c","schema_version":"1.0","event_id":"sha256:b2f3af7a7d4a6b71fb07a9d9a6f560c95cedfb94ac682e6f4300cf131453913c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ/bundle.json","state_url":"https://pith.science/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T15:02:38Z","links":{"resolver":"https://pith.science/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ","bundle":"https://pith.science/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ/bundle.json","state":"https://pith.science/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PPOHL44E4LDOZW3WFSH3ADYVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4PPOHL44E4LDOZW3WFSH3ADYVQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"860f84d7083c303569709f9a255f5d52f4a3d9a014b07d87d65f70a27e8bf3cb","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T14:13:09Z","title_canon_sha256":"7897101965bbeb7f5693585ef96407a31ecedc78f6769da4d5b2a6d2607805e8"},"schema_version":"1.0","source":{"id":"2607.19126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19126","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19126v1","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19126","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"4PPOHL44E4LD","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"pith_short_16","alias_value":"4PPOHL44E4LDOZW3","created_at":"2026-07-22T01:24:09Z"},{"alias_kind":"pith_short_8","alias_value":"4PPOHL44","created_at":"2026-07-22T01:24:09Z"}],"graph_snapshots":[{"event_id":"sha256:b2f3af7a7d4a6b71fb07a9d9a6f560c95cedfb94ac682e6f4300cf131453913c","target":"graph","created_at":"2026-07-22T01:24:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.19126/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noi","authors_text":"Giuseppe Marra, Ondrej Kuzelka, Peter Jung","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T14:13:09Z","title":"Parallel Noising in Neural Markov Logic Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19126","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d423a145ee3ff13eaa2e2116b9cbb26c911c8fe804b5c4803e8343ad79202a93","target":"record","created_at":"2026-07-22T01:24:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"860f84d7083c303569709f9a255f5d52f4a3d9a014b07d87d65f70a27e8bf3cb","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T14:13:09Z","title_canon_sha256":"7897101965bbeb7f5693585ef96407a31ecedc78f6769da4d5b2a6d2607805e8"},"schema_version":"1.0","source":{"id":"2607.19126","kind":"arxiv","version":1}},"canonical_sha256":"e3dee3af9c27163766dbb1647d8078ac37b785d2208f6743fe1f6b4890546722","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3dee3af9c27163766dbb1647d8078ac37b785d2208f6743fe1f6b4890546722","first_computed_at":"2026-07-22T01:24:09.930692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:24:09.930692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o1xG34MtuAEc6QKxmsNqz/IJ4nbNFHPA7WuRivrz+wNOZQdgj7EtCqLUFd4foyzz4trSBthc0EQ1NJ9ew4HyAA==","signature_status":"signed_v1","signed_at":"2026-07-22T01:24:09.931603Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d423a145ee3ff13eaa2e2116b9cbb26c911c8fe804b5c4803e8343ad79202a93","sha256:b2f3af7a7d4a6b71fb07a9d9a6f560c95cedfb94ac682e6f4300cf131453913c"],"state_sha256":"5f1e3ae1dc340941c2b491f53edf6102d6bb31dbf2f06235f96ebcc97c6b64b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmzZo44BnRb0u2DqP373jRKHDEGoPKwYT3DGvAjXms+T2yhG3uBpjHKtDh/uI00byTlZEnTAN8Cffv+Ys5D6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:02:38.307699Z","bundle_sha256":"ee34d871ba189fc999100ace012dfca5b18df07794d838e02ae3f6c25729cffd"}}