{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NNSBOKSIFNYW2NMPFJCW2XQOLW","short_pith_number":"pith:NNSBOKSI","canonical_record":{"source":{"id":"1110.6549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-29T19:47:59Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"62f0dffc82e5571e7208ba9b88ff2abbecc5601acb1da62cb43a073f523fc70e","abstract_canon_sha256":"6b2dae70123d29a6e7e5aed40d8cce12bc85bf612258d2e53c88e512d3241b93"},"schema_version":"1.0"},"canonical_sha256":"6b64172a482b716d358f2a456d5e0e5d90f8512bff0a882bd5a0f0f6f48e47cf","source":{"kind":"arxiv","id":"1110.6549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6549","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6549v1","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6549","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"NNSBOKSIFNYW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NNSBOKSIFNYW2NMP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NNSBOKSI","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NNSBOKSIFNYW2NMPFJCW2XQOLW","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-29T19:47:59Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"62f0dffc82e5571e7208ba9b88ff2abbecc5601acb1da62cb43a073f523fc70e","abstract_canon_sha256":"6b2dae70123d29a6e7e5aed40d8cce12bc85bf612258d2e53c88e512d3241b93"},"schema_version":"1.0"},"canonical_sha256":"6b64172a482b716d358f2a456d5e0e5d90f8512bff0a882bd5a0f0f6f48e47cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:03.310921Z","signature_b64":"E0ThC1jZSu6z6bu6UzQkmPDlxAMMmxnStX58wdAyDsxSEokPRuakPYRIQ1pDOYpGKeDVzQXqRQZnSxGjkuPPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b64172a482b716d358f2a456d5e0e5d90f8512bff0a882bd5a0f0f6f48e47cf","last_reissued_at":"2026-05-18T04:08:03.310471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:03.310471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6549","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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZuVt8AAQ75YeZ7hTz1AqzoY7GI2aTVGpqm1qJjByREHglaXgvL7mG6cMJE8dfI8kKMIpTgqFfpGusS6MP6xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:34:47.126684Z"},"content_sha256":"ae693be36591a1b46f281f68b37e1b5204b4cac8db7e65f594b4752b133423a2","schema_version":"1.0","event_id":"sha256:ae693be36591a1b46f281f68b37e1b5204b4cac8db7e65f594b4752b133423a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NNSBOKSIFNYW2NMPFJCW2XQOLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonic Local Decay Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Avy Soffer","submitted_at":"2011-10-29T19:47:59Z","abstract_excerpt":"For the Hamiltonian operator H = -{\\Delta}+V(x) of the Schr\\\"odinger Equation with a repulsive potential, the problem of local decay is considered. It is analyzed by a direct method, based on a new, L^2 bounded, propagation observable. The resulting decay estimate, is in certain cases monotonic in time, with no \"Quantum Corrections\". This method is then applied to some examples in one and higher dimensions. In particular the case of the Wave Equation on a Schwarzschild manifold is redone: Local decay, stronger than the known ones are proved (minimal loss of angular derivatives and lower order "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6549","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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5WKxAxRE/ugZB35DcdNsdXT0l8cnjT4JnLMxbQlb7PZLrqLPv6T8vg5p0apJzjVo1L5Th8d8xGVrRo01Vj+0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:34:47.127035Z"},"content_sha256":"a33cdcabda07ef2704de9382987f84b6b97d43693cd97a9a668715204493bf72","schema_version":"1.0","event_id":"sha256:a33cdcabda07ef2704de9382987f84b6b97d43693cd97a9a668715204493bf72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW/bundle.json","state_url":"https://pith.science/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW/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":"2026-06-02T20:34:47Z","links":{"resolver":"https://pith.science/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW","bundle":"https://pith.science/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW/bundle.json","state":"https://pith.science/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNSBOKSIFNYW2NMPFJCW2XQOLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NNSBOKSIFNYW2NMPFJCW2XQOLW","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":"6b2dae70123d29a6e7e5aed40d8cce12bc85bf612258d2e53c88e512d3241b93","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-29T19:47:59Z","title_canon_sha256":"62f0dffc82e5571e7208ba9b88ff2abbecc5601acb1da62cb43a073f523fc70e"},"schema_version":"1.0","source":{"id":"1110.6549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6549","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6549v1","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6549","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"NNSBOKSIFNYW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NNSBOKSIFNYW2NMP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NNSBOKSI","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:a33cdcabda07ef2704de9382987f84b6b97d43693cd97a9a668715204493bf72","target":"graph","created_at":"2026-05-18T04:08:03Z","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":"For the Hamiltonian operator H = -{\\Delta}+V(x) of the Schr\\\"odinger Equation with a repulsive potential, the problem of local decay is considered. It is analyzed by a direct method, based on a new, L^2 bounded, propagation observable. The resulting decay estimate, is in certain cases monotonic in time, with no \"Quantum Corrections\". This method is then applied to some examples in one and higher dimensions. In particular the case of the Wave Equation on a Schwarzschild manifold is redone: Local decay, stronger than the known ones are proved (minimal loss of angular derivatives and lower order ","authors_text":"Avy Soffer","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-29T19:47:59Z","title":"Monotonic Local Decay Estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6549","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:ae693be36591a1b46f281f68b37e1b5204b4cac8db7e65f594b4752b133423a2","target":"record","created_at":"2026-05-18T04:08:03Z","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":"6b2dae70123d29a6e7e5aed40d8cce12bc85bf612258d2e53c88e512d3241b93","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-29T19:47:59Z","title_canon_sha256":"62f0dffc82e5571e7208ba9b88ff2abbecc5601acb1da62cb43a073f523fc70e"},"schema_version":"1.0","source":{"id":"1110.6549","kind":"arxiv","version":1}},"canonical_sha256":"6b64172a482b716d358f2a456d5e0e5d90f8512bff0a882bd5a0f0f6f48e47cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b64172a482b716d358f2a456d5e0e5d90f8512bff0a882bd5a0f0f6f48e47cf","first_computed_at":"2026-05-18T04:08:03.310471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:03.310471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E0ThC1jZSu6z6bu6UzQkmPDlxAMMmxnStX58wdAyDsxSEokPRuakPYRIQ1pDOYpGKeDVzQXqRQZnSxGjkuPPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:03.310921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae693be36591a1b46f281f68b37e1b5204b4cac8db7e65f594b4752b133423a2","sha256:a33cdcabda07ef2704de9382987f84b6b97d43693cd97a9a668715204493bf72"],"state_sha256":"c7ab7b6f52b681c3b186562bc21847a1b5bed1a61700556639fde85b9b0d7639"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PSltG5i8NTLoxA0Gm+2gC+16apqzfhoYqwGHPTg+rk3iucxKBNlXBCjR62OTAIZ2mq43N7cOHLn/tR0pn0NKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:34:47.129294Z","bundle_sha256":"5d6cf11960db0d8ed5ebc323461e4541edb78c6e23b04971fad04cf2b23f26b0"}}