{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NKEAI7JFBYXHFHZJFXC7O6CZFL","short_pith_number":"pith:NKEAI7JF","canonical_record":{"source":{"id":"2512.10499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-11T10:21:06Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d543c520523da1a30e44e4360b1061b7da2e13f489fea64502a9a09693e579c2","abstract_canon_sha256":"0a9e1ee45e4fcd4e22f7cecb29cfd9b7f2ca9a9302731e1f36367f53259bed19"},"schema_version":"1.0"},"canonical_sha256":"6a88047d250e2e729f292dc5f778592aeba5fd6c8613c19c8c1a0b103db240a1","source":{"kind":"arxiv","id":"2512.10499","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.10499","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"2512.10499v2","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.10499","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"NKEAI7JFBYXH","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"pith_short_16","alias_value":"NKEAI7JFBYXHFHZJ","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"pith_short_8","alias_value":"NKEAI7JF","created_at":"2026-05-20T00:00:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NKEAI7JFBYXHFHZJFXC7O6CZFL","target":"record","payload":{"canonical_record":{"source":{"id":"2512.10499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-11T10:21:06Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d543c520523da1a30e44e4360b1061b7da2e13f489fea64502a9a09693e579c2","abstract_canon_sha256":"0a9e1ee45e4fcd4e22f7cecb29cfd9b7f2ca9a9302731e1f36367f53259bed19"},"schema_version":"1.0"},"canonical_sha256":"6a88047d250e2e729f292dc5f778592aeba5fd6c8613c19c8c1a0b103db240a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:30.037976Z","signature_b64":"RDiJTCzrMBEH125qyDWC6v7zKY+VZgyIvekJGG/Zuu6BLOagAGYBdELUbH1KNGVln8IZgy0o4IxgikFrPP9MBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a88047d250e2e729f292dc5f778592aeba5fd6c8613c19c8c1a0b103db240a1","last_reissued_at":"2026-05-20T00:00:30.037443Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:30.037443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.10499","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4luNCxvbWMwZ7B1F245CrnP/4mtRq5jrW8uBkuauRcbkc4iZ+30n9rRnn6ChrhMsYDe1dtKWWx1fRg4paQ7RDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:42:35.347176Z"},"content_sha256":"c069156d65bd01032a3da63eca39f6c5968fc68834caa32d61c789e9aa5a256a","schema_version":"1.0","event_id":"sha256:c069156d65bd01032a3da63eca39f6c5968fc68834caa32d61c789e9aa5a256a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NKEAI7JFBYXHFHZJFXC7O6CZFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Three-Dimensional SFT with Sparse Columns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.DS","authors_text":"Ilkka T\\\"orm\\\"a, Ville Salo","submitted_at":"2025-12-11T10:21:06Z","abstract_excerpt":"We construct a nontrivial three-dimensional subshift of finite type whose projective $\\Z$-subdynamics, or $\\Z$-trace, is 2-sparse, meaning that there are at most two nonzero symbols in any vertical column. The subshift is deterministic in the direction of the subdynamics, so it is topologically conjugate to the set of spacetime diagrams of a partial cellular automaton. We also present a variant of the subshift that is defined by Wang cubes, and one whose alphabet is binary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.10499","kind":"arxiv","version":2},"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/2512.10499/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":"2026-05-20T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4LdQHBPzM3kdW91vQrlxhu6449/sn4dBjmOumwEQU7OwZ5ZlrxZdvmuSpfhjWAtHNuGaeJefiV9bJfppZOUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:42:35.347960Z"},"content_sha256":"af06224e924e72c26747bbc8f2f34a72e0b20f525dca59e0e064f0b486e756e1","schema_version":"1.0","event_id":"sha256:af06224e924e72c26747bbc8f2f34a72e0b20f525dca59e0e064f0b486e756e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL/bundle.json","state_url":"https://pith.science/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL/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":"2026-06-09T03:42:35Z","links":{"resolver":"https://pith.science/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL","bundle":"https://pith.science/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL/bundle.json","state":"https://pith.science/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKEAI7JFBYXHFHZJFXC7O6CZFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NKEAI7JFBYXHFHZJFXC7O6CZFL","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":"0a9e1ee45e4fcd4e22f7cecb29cfd9b7f2ca9a9302731e1f36367f53259bed19","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-11T10:21:06Z","title_canon_sha256":"d543c520523da1a30e44e4360b1061b7da2e13f489fea64502a9a09693e579c2"},"schema_version":"1.0","source":{"id":"2512.10499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.10499","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"2512.10499v2","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.10499","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"NKEAI7JFBYXH","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"pith_short_16","alias_value":"NKEAI7JFBYXHFHZJ","created_at":"2026-05-20T00:00:30Z"},{"alias_kind":"pith_short_8","alias_value":"NKEAI7JF","created_at":"2026-05-20T00:00:30Z"}],"graph_snapshots":[{"event_id":"sha256:af06224e924e72c26747bbc8f2f34a72e0b20f525dca59e0e064f0b486e756e1","target":"graph","created_at":"2026-05-20T00:00:30Z","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/2512.10499/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a nontrivial three-dimensional subshift of finite type whose projective $\\Z$-subdynamics, or $\\Z$-trace, is 2-sparse, meaning that there are at most two nonzero symbols in any vertical column. The subshift is deterministic in the direction of the subdynamics, so it is topologically conjugate to the set of spacetime diagrams of a partial cellular automaton. We also present a variant of the subshift that is defined by Wang cubes, and one whose alphabet is binary.","authors_text":"Ilkka T\\\"orm\\\"a, Ville Salo","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-11T10:21:06Z","title":"A Three-Dimensional SFT with Sparse Columns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.10499","kind":"arxiv","version":2},"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:c069156d65bd01032a3da63eca39f6c5968fc68834caa32d61c789e9aa5a256a","target":"record","created_at":"2026-05-20T00:00:30Z","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":"0a9e1ee45e4fcd4e22f7cecb29cfd9b7f2ca9a9302731e1f36367f53259bed19","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-12-11T10:21:06Z","title_canon_sha256":"d543c520523da1a30e44e4360b1061b7da2e13f489fea64502a9a09693e579c2"},"schema_version":"1.0","source":{"id":"2512.10499","kind":"arxiv","version":2}},"canonical_sha256":"6a88047d250e2e729f292dc5f778592aeba5fd6c8613c19c8c1a0b103db240a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a88047d250e2e729f292dc5f778592aeba5fd6c8613c19c8c1a0b103db240a1","first_computed_at":"2026-05-20T00:00:30.037443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:30.037443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RDiJTCzrMBEH125qyDWC6v7zKY+VZgyIvekJGG/Zuu6BLOagAGYBdELUbH1KNGVln8IZgy0o4IxgikFrPP9MBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:30.037976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.10499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c069156d65bd01032a3da63eca39f6c5968fc68834caa32d61c789e9aa5a256a","sha256:af06224e924e72c26747bbc8f2f34a72e0b20f525dca59e0e064f0b486e756e1"],"state_sha256":"739cb1b635794c991235ed2563245b1e558154bc7b4addfe7bd910fa8a319baa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvHnCZLMPoDWcqcdphqzShL5nquydOkZ/G4QOu/RveNnXHythwb76NAV7gChfWr6IN78LqH7d/SzW2ojGbxWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:42:35.351950Z","bundle_sha256":"55ea1a6ab7af2d33e253d3941a6f4241190e45f62389b148aaf3aaa7b0b6f81d"}}