{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:PSQCKJ4PBS6DAEVQYIW2EX2LQS","short_pith_number":"pith:PSQCKJ4P","canonical_record":{"source":{"id":"hep-th/0306092","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-06-10T21:18:23Z","cross_cats_sorted":[],"title_canon_sha256":"8698a078e990ad520ed20def2ef43535216b9151c9f8f0945601f6ced2701b36","abstract_canon_sha256":"84cc5fcfe42f7d7c978d4538f937829a062f742e93cc3128bfb13c5dd6f84992"},"schema_version":"1.0"},"canonical_sha256":"7ca025278f0cbc3012b0c22da25f4b84b7551e58f080babbf59e1e2d5d9f00a8","source":{"kind":"arxiv","id":"hep-th/0306092","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0306092","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0306092v1","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0306092","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"PSQCKJ4PBS6D","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_16","alias_value":"PSQCKJ4PBS6DAEVQ","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_8","alias_value":"PSQCKJ4P","created_at":"2026-07-04T14:31:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:PSQCKJ4PBS6DAEVQYIW2EX2LQS","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0306092","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-06-10T21:18:23Z","cross_cats_sorted":[],"title_canon_sha256":"8698a078e990ad520ed20def2ef43535216b9151c9f8f0945601f6ced2701b36","abstract_canon_sha256":"84cc5fcfe42f7d7c978d4538f937829a062f742e93cc3128bfb13c5dd6f84992"},"schema_version":"1.0"},"canonical_sha256":"7ca025278f0cbc3012b0c22da25f4b84b7551e58f080babbf59e1e2d5d9f00a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:31:58.637906Z","signature_b64":"oecqknCMXRbSzhdkIXXLW6We43pTHm7ptU3zw8AhYY3y4Em20Jxrf3A90U0nNhB8BOGHMTHF+OgMDrmQyEp0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ca025278f0cbc3012b0c22da25f4b84b7551e58f080babbf59e1e2d5d9f00a8","last_reissued_at":"2026-07-04T14:31:58.637549Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:31:58.637549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0306092","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":"2026-07-04T14:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRHpqanm01eMGp7Oiw3pTTjAUdTZCDC8Rr2WsiPDTdf7+sU29ZJlmRazWWNJfOsPFO49QqtUlriONQzKSuYMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T01:11:27.925558Z"},"content_sha256":"05f12b38f22bb45f2b22919312019de5be6e469a812b49c66f09598b599cf3c3","schema_version":"1.0","event_id":"sha256:05f12b38f22bb45f2b22919312019de5be6e469a812b49c66f09598b599cf3c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:PSQCKJ4PBS6DAEVQYIW2EX2LQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality Walls, Duality Trees and Fractional Branes","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amihay Hanany, Pavlos Kazakopoulos, Sebastian Franco, Yang-Hui He","submitted_at":"2003-06-10T21:18:23Z","abstract_excerpt":"We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0306092","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/hep-th/0306092/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":"2026-07-04T14:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yL7hEVHY9yPtGpMLlVs053SWZiqlfOZYXbs8nZM0ZdrNoFYQthhcBtcvcxGXrcrthaNL3Aym/q5Dc6WD7o+hAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T01:11:27.926157Z"},"content_sha256":"2e4ae5b14c9b56bdbe394829103b828a044e1e1011fbfad36230570aa53bdab4","schema_version":"1.0","event_id":"sha256:2e4ae5b14c9b56bdbe394829103b828a044e1e1011fbfad36230570aa53bdab4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS/bundle.json","state_url":"https://pith.science/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS/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":"2026-08-03T01:11:27Z","links":{"resolver":"https://pith.science/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS","bundle":"https://pith.science/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS/bundle.json","state":"https://pith.science/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSQCKJ4PBS6DAEVQYIW2EX2LQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:PSQCKJ4PBS6DAEVQYIW2EX2LQS","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":"84cc5fcfe42f7d7c978d4538f937829a062f742e93cc3128bfb13c5dd6f84992","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-06-10T21:18:23Z","title_canon_sha256":"8698a078e990ad520ed20def2ef43535216b9151c9f8f0945601f6ced2701b36"},"schema_version":"1.0","source":{"id":"hep-th/0306092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0306092","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0306092v1","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0306092","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"PSQCKJ4PBS6D","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_16","alias_value":"PSQCKJ4PBS6DAEVQ","created_at":"2026-07-04T14:31:58Z"},{"alias_kind":"pith_short_8","alias_value":"PSQCKJ4P","created_at":"2026-07-04T14:31:58Z"}],"graph_snapshots":[{"event_id":"sha256:2e4ae5b14c9b56bdbe394829103b828a044e1e1011fbfad36230570aa53bdab4","target":"graph","created_at":"2026-07-04T14:31:58Z","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/hep-th/0306092/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at wh","authors_text":"Amihay Hanany, Pavlos Kazakopoulos, Sebastian Franco, Yang-Hui He","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-06-10T21:18:23Z","title":"Duality Walls, Duality Trees and Fractional Branes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0306092","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":"sha256:05f12b38f22bb45f2b22919312019de5be6e469a812b49c66f09598b599cf3c3","target":"record","created_at":"2026-07-04T14:31:58Z","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":"84cc5fcfe42f7d7c978d4538f937829a062f742e93cc3128bfb13c5dd6f84992","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-06-10T21:18:23Z","title_canon_sha256":"8698a078e990ad520ed20def2ef43535216b9151c9f8f0945601f6ced2701b36"},"schema_version":"1.0","source":{"id":"hep-th/0306092","kind":"arxiv","version":1}},"canonical_sha256":"7ca025278f0cbc3012b0c22da25f4b84b7551e58f080babbf59e1e2d5d9f00a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ca025278f0cbc3012b0c22da25f4b84b7551e58f080babbf59e1e2d5d9f00a8","first_computed_at":"2026-07-04T14:31:58.637549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:31:58.637549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oecqknCMXRbSzhdkIXXLW6We43pTHm7ptU3zw8AhYY3y4Em20Jxrf3A90U0nNhB8BOGHMTHF+OgMDrmQyEp0Bg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:31:58.637906Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0306092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05f12b38f22bb45f2b22919312019de5be6e469a812b49c66f09598b599cf3c3","sha256:2e4ae5b14c9b56bdbe394829103b828a044e1e1011fbfad36230570aa53bdab4"],"state_sha256":"e594ce4887e67dc6b1a435d6c84e06974e335a4c41fb18baf8fa2eccc79b90b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNWo0YBM9lm9CADV1mkuB+8F6GX1Cus2eXHXw/47nLRSXNWrI4gZpKhwDTzTp7log0atkxkcZovSB/Ra4N3nDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T01:11:27.931201Z","bundle_sha256":"05cdf7bace40df3bc85c99f6af807d422cc0e712c5e1dcfde587d093d927a139"}}