{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HXWFD6VKEHEHWO4YOL7KQBKRTB","short_pith_number":"pith:HXWFD6VK","canonical_record":{"source":{"id":"1510.07324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-25T23:38:48Z","cross_cats_sorted":["math.CA","math.OA","math.SP"],"title_canon_sha256":"07d62a69e050af93cae4f92ae3d0c0ce9031533b647bc44733b143eb24529ad3","abstract_canon_sha256":"7727d8486b1bebb6cd275cb29d55eef697691c2d454516dfa009ab21cc5eabeb"},"schema_version":"1.0"},"canonical_sha256":"3dec51faaa21c87b3b9872fea805519858bb1b2ffe3c1351dcd9901d6a641748","source":{"kind":"arxiv","id":"1510.07324","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07324","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07324v2","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07324","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"HXWFD6VKEHEH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HXWFD6VKEHEHWO4Y","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HXWFD6VK","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HXWFD6VKEHEHWO4YOL7KQBKRTB","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-25T23:38:48Z","cross_cats_sorted":["math.CA","math.OA","math.SP"],"title_canon_sha256":"07d62a69e050af93cae4f92ae3d0c0ce9031533b647bc44733b143eb24529ad3","abstract_canon_sha256":"7727d8486b1bebb6cd275cb29d55eef697691c2d454516dfa009ab21cc5eabeb"},"schema_version":"1.0"},"canonical_sha256":"3dec51faaa21c87b3b9872fea805519858bb1b2ffe3c1351dcd9901d6a641748","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:57.794104Z","signature_b64":"uH9Lk82ORrzMDW67nvCmHLDuzDjkrlToamySpsgGpMIRDyn5e5zAaX6x0xKiPfIcS+CjhAIHF6dLS6br1OEgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dec51faaa21c87b3b9872fea805519858bb1b2ffe3c1351dcd9901d6a641748","last_reissued_at":"2026-05-18T01:04:57.793412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:57.793412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07324","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":"2026-05-18T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8BfZqJLdBi14TKrFNguAv/ZbgFDq4Dma8FJCj9X2VRc6x/Hr+6X5MVMmNFFaHhmofQsOuNEBN2HsnI/gTTw/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:22:46.060827Z"},"content_sha256":"0d05154e94be9c981c08af44879e7c10f8e68616d322dc11263f6374bb301cbb","schema_version":"1.0","event_id":"sha256:0d05154e94be9c981c08af44879e7c10f8e68616d322dc11263f6374bb301cbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HXWFD6VKEHEHWO4YOL7KQBKRTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalized Kontsevich-Vishik trace for Fourier Integral Operators and the Laurent expansion of $\\zeta$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OA","math.SP"],"primary_cat":"math.AP","authors_text":"Simon Scott, Tobias Hartung","submitted_at":"2015-10-25T23:38:48Z","abstract_excerpt":"Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\\log$-homogeneous distribution as an approach to $\\zeta$-functions for a class of Fourier Integral Operators which includes cases of amplitudes with asymptotic expansion $\\sum_{k\\in\\mathbb{N}}a_{m_k}$ where each $a_{m_k}$ is $\\log$-homogeneous with degree of homogeneity $m_k$ but violating $\\Re(m_k)\\to-\\infty$. We will calculate the Laurent expansion for the $\\zeta$-function and give formulae for the coefficients in terms of the phase function and amplitude as well as investigate generalizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07324","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":""},"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":"2026-05-18T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ax/ErgIoOCGh3dw89MBLTnvzHWNLIBY4Fs843Fd7e3OXNZVInd0xd/zFOWWktsSgRpVOPOd0Re8iaycciQsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:22:46.061361Z"},"content_sha256":"423acbdafbda87255ba6e8a78820dad98bc66d478033215da6a490dd21928e49","schema_version":"1.0","event_id":"sha256:423acbdafbda87255ba6e8a78820dad98bc66d478033215da6a490dd21928e49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB/bundle.json","state_url":"https://pith.science/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB/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":"2026-05-27T19:22:46Z","links":{"resolver":"https://pith.science/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB","bundle":"https://pith.science/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB/bundle.json","state":"https://pith.science/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXWFD6VKEHEHWO4YOL7KQBKRTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HXWFD6VKEHEHWO4YOL7KQBKRTB","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":"7727d8486b1bebb6cd275cb29d55eef697691c2d454516dfa009ab21cc5eabeb","cross_cats_sorted":["math.CA","math.OA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-25T23:38:48Z","title_canon_sha256":"07d62a69e050af93cae4f92ae3d0c0ce9031533b647bc44733b143eb24529ad3"},"schema_version":"1.0","source":{"id":"1510.07324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07324","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07324v2","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07324","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"HXWFD6VKEHEH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HXWFD6VKEHEHWO4Y","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HXWFD6VK","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:423acbdafbda87255ba6e8a78820dad98bc66d478033215da6a490dd21928e49","target":"graph","created_at":"2026-05-18T01:04:57Z","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":"Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\\log$-homogeneous distribution as an approach to $\\zeta$-functions for a class of Fourier Integral Operators which includes cases of amplitudes with asymptotic expansion $\\sum_{k\\in\\mathbb{N}}a_{m_k}$ where each $a_{m_k}$ is $\\log$-homogeneous with degree of homogeneity $m_k$ but violating $\\Re(m_k)\\to-\\infty$. We will calculate the Laurent expansion for the $\\zeta$-function and give formulae for the coefficients in terms of the phase function and amplitude as well as investigate generalizatio","authors_text":"Simon Scott, Tobias Hartung","cross_cats":["math.CA","math.OA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-25T23:38:48Z","title":"A generalized Kontsevich-Vishik trace for Fourier Integral Operators and the Laurent expansion of $\\zeta$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07324","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":"sha256:0d05154e94be9c981c08af44879e7c10f8e68616d322dc11263f6374bb301cbb","target":"record","created_at":"2026-05-18T01:04:57Z","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":"7727d8486b1bebb6cd275cb29d55eef697691c2d454516dfa009ab21cc5eabeb","cross_cats_sorted":["math.CA","math.OA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-25T23:38:48Z","title_canon_sha256":"07d62a69e050af93cae4f92ae3d0c0ce9031533b647bc44733b143eb24529ad3"},"schema_version":"1.0","source":{"id":"1510.07324","kind":"arxiv","version":2}},"canonical_sha256":"3dec51faaa21c87b3b9872fea805519858bb1b2ffe3c1351dcd9901d6a641748","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dec51faaa21c87b3b9872fea805519858bb1b2ffe3c1351dcd9901d6a641748","first_computed_at":"2026-05-18T01:04:57.793412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:57.793412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uH9Lk82ORrzMDW67nvCmHLDuzDjkrlToamySpsgGpMIRDyn5e5zAaX6x0xKiPfIcS+CjhAIHF6dLS6br1OEgCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:57.794104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d05154e94be9c981c08af44879e7c10f8e68616d322dc11263f6374bb301cbb","sha256:423acbdafbda87255ba6e8a78820dad98bc66d478033215da6a490dd21928e49"],"state_sha256":"14e6ccaded9f9099c050367d5035d99f6879a0b6e535274bf2fc617a61d1ddfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/mX3Qsz2eqOZ8mcKQvLtCs+XK0845h6uh2cSyW4Kef5A65jSMX986at0UvO1bIouvPSponLqUh3laRln4fiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:22:46.063755Z","bundle_sha256":"e50285241497e0f5e11063ab62e7ced1291da57be43c106c992b69c3af107d0e"}}