{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EZMUBAJDEQ2K25TGFJQB33TP6U","short_pith_number":"pith:EZMUBAJD","canonical_record":{"source":{"id":"0909.2868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-09-16T19:08:08Z","cross_cats_sorted":[],"title_canon_sha256":"d28ebcb7fa5b4c9eb84c59c3c8341821cf183f2a6475d3eac0a1f7d03492a3c0","abstract_canon_sha256":"1fc673c0838f0fe6a476abbc0d3a77298366584e1af12a56d4d8fa1755581cc0"},"schema_version":"1.0"},"canonical_sha256":"26594081232434ad76662a601dee6ff50b6bea5501b026aac792cf357ca69b17","source":{"kind":"arxiv","id":"0909.2868","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2868","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2868v1","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2868","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"EZMUBAJDEQ2K","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EZMUBAJDEQ2K25TG","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EZMUBAJD","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EZMUBAJDEQ2K25TGFJQB33TP6U","target":"record","payload":{"canonical_record":{"source":{"id":"0909.2868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-09-16T19:08:08Z","cross_cats_sorted":[],"title_canon_sha256":"d28ebcb7fa5b4c9eb84c59c3c8341821cf183f2a6475d3eac0a1f7d03492a3c0","abstract_canon_sha256":"1fc673c0838f0fe6a476abbc0d3a77298366584e1af12a56d4d8fa1755581cc0"},"schema_version":"1.0"},"canonical_sha256":"26594081232434ad76662a601dee6ff50b6bea5501b026aac792cf357ca69b17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:27.289205Z","signature_b64":"7jkt204TMfMYzJSd9m+c08FCZiftgkEw2q0Y1nGanPMauDLV3wxv2SUQ6Urb2S0iyU7PMFUmZA0u1RZxddmdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26594081232434ad76662a601dee6ff50b6bea5501b026aac792cf357ca69b17","last_reissued_at":"2026-05-18T04:33:27.288766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:27.288766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.2868","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":"2026-05-18T04:33:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OvCg/sjHrzaintSENlY7AWA+q7mBzOGWi+I+mnFu2uTAFO+GpAFiHTaAl6vCJjzqawfrcG3Fhu2am+G7pnhUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:01:46.654533Z"},"content_sha256":"fd629af83862e7da00b2e51ed1aa6801ea4d57a1066dd91243d3c5c82ec5ba27","schema_version":"1.0","event_id":"sha256:fd629af83862e7da00b2e51ed1aa6801ea4d57a1066dd91243d3c5c82ec5ba27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EZMUBAJDEQ2K25TGFJQB33TP6U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Classification of Brane Tilings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amihay Hanany, John Davey, Jurgis Pasukonis","submitted_at":"2009-09-16T19:08:08Z","abstract_excerpt":"We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2868","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":""},"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":"2026-05-18T04:33:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6G1uU7BSVTit/lwaMlIWIKtkSh3UAFymyb5xHDzgzQHE7NOA1Y2NDKRix+EDJfCz5ccQYwLzKCU9RAJlO3xyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:01:46.654993Z"},"content_sha256":"0eb2a7ed5d54dae6112cd3b4b66568f0cca396aee7a27fa2069f4cb72a982205","schema_version":"1.0","event_id":"sha256:0eb2a7ed5d54dae6112cd3b4b66568f0cca396aee7a27fa2069f4cb72a982205"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZMUBAJDEQ2K25TGFJQB33TP6U/bundle.json","state_url":"https://pith.science/pith/EZMUBAJDEQ2K25TGFJQB33TP6U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZMUBAJDEQ2K25TGFJQB33TP6U/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":"2026-08-12T09:01:46Z","links":{"resolver":"https://pith.science/pith/EZMUBAJDEQ2K25TGFJQB33TP6U","bundle":"https://pith.science/pith/EZMUBAJDEQ2K25TGFJQB33TP6U/bundle.json","state":"https://pith.science/pith/EZMUBAJDEQ2K25TGFJQB33TP6U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZMUBAJDEQ2K25TGFJQB33TP6U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EZMUBAJDEQ2K25TGFJQB33TP6U","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":"1fc673c0838f0fe6a476abbc0d3a77298366584e1af12a56d4d8fa1755581cc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-09-16T19:08:08Z","title_canon_sha256":"d28ebcb7fa5b4c9eb84c59c3c8341821cf183f2a6475d3eac0a1f7d03492a3c0"},"schema_version":"1.0","source":{"id":"0909.2868","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2868","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2868v1","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2868","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"EZMUBAJDEQ2K","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EZMUBAJDEQ2K25TG","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EZMUBAJD","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:0eb2a7ed5d54dae6112cd3b4b66568f0cca396aee7a27fa2069f4cb72a982205","target":"graph","created_at":"2026-05-18T04:33:27Z","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"},"paper":{"abstract_excerpt":"We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most com","authors_text":"Amihay Hanany, John Davey, Jurgis Pasukonis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-09-16T19:08:08Z","title":"On the Classification of Brane Tilings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2868","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:fd629af83862e7da00b2e51ed1aa6801ea4d57a1066dd91243d3c5c82ec5ba27","target":"record","created_at":"2026-05-18T04:33:27Z","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":"1fc673c0838f0fe6a476abbc0d3a77298366584e1af12a56d4d8fa1755581cc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-09-16T19:08:08Z","title_canon_sha256":"d28ebcb7fa5b4c9eb84c59c3c8341821cf183f2a6475d3eac0a1f7d03492a3c0"},"schema_version":"1.0","source":{"id":"0909.2868","kind":"arxiv","version":1}},"canonical_sha256":"26594081232434ad76662a601dee6ff50b6bea5501b026aac792cf357ca69b17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26594081232434ad76662a601dee6ff50b6bea5501b026aac792cf357ca69b17","first_computed_at":"2026-05-18T04:33:27.288766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:27.288766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7jkt204TMfMYzJSd9m+c08FCZiftgkEw2q0Y1nGanPMauDLV3wxv2SUQ6Urb2S0iyU7PMFUmZA0u1RZxddmdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:27.289205Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2868","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd629af83862e7da00b2e51ed1aa6801ea4d57a1066dd91243d3c5c82ec5ba27","sha256:0eb2a7ed5d54dae6112cd3b4b66568f0cca396aee7a27fa2069f4cb72a982205"],"state_sha256":"a02910aa3dd0c5d448a987031ea216b33d77ebf88715d58c8bc8b27e3968c118"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3a3FpmrjHMqp+O/3synCuS//arufybga74INt5uB8kFp+XFUKMCygGOvmghfQLI/paaa7UHgi+FztvybhCZFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T09:01:46.658591Z","bundle_sha256":"01d72348b9d741e5fb1b91048133631c0ed405af37c90549402778daf28f2708"}}