{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KUO7VUAM7EHETBRBNKBHVKDN37","short_pith_number":"pith:KUO7VUAM","canonical_record":{"source":{"id":"2509.26274","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-30T13:58:28Z","cross_cats_sorted":["cond-mat.str-el","cs.NA"],"title_canon_sha256":"6aa3cfea5abf1428524d7a6fe27515f933c890ca21ee7b3a0ec66772e2e329a8","abstract_canon_sha256":"0777cb5ece166b03e15ebf0a192be6951640df0b723214a08b2cd21977fbac2f"},"schema_version":"1.0"},"canonical_sha256":"551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126","source":{"kind":"arxiv","id":"2509.26274","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.26274","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"arxiv_version","alias_value":"2509.26274v3","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.26274","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_12","alias_value":"KUO7VUAM7EHE","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_16","alias_value":"KUO7VUAM7EHETBRB","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_8","alias_value":"KUO7VUAM","created_at":"2026-06-19T16:10:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KUO7VUAM7EHETBRBNKBHVKDN37","target":"record","payload":{"canonical_record":{"source":{"id":"2509.26274","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-30T13:58:28Z","cross_cats_sorted":["cond-mat.str-el","cs.NA"],"title_canon_sha256":"6aa3cfea5abf1428524d7a6fe27515f933c890ca21ee7b3a0ec66772e2e329a8","abstract_canon_sha256":"0777cb5ece166b03e15ebf0a192be6951640df0b723214a08b2cd21977fbac2f"},"schema_version":"1.0"},"canonical_sha256":"551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:31.462776Z","signature_b64":"EBLVwogGtSAKAIXWCZosibW2tkrvlh7GJLIL5ObTd5EzQAxG3FZa9X/uruoGMIdnOfhmJ9Y3ZE3mdJ6wZIpWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126","last_reissued_at":"2026-06-19T16:10:31.462326Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:31.462326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.26274","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhz5pNcTYGd4CN72JH2Sx8iKyRL9XxbTJoRIlzujgg+ROC/IdnV7PHPxV0PaG8VZ3ZuYlxWh1LNu8swm39VEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:48:28.400574Z"},"content_sha256":"17c90017c7437d83112bb56d3451d977e09994e250dd1a6cdb8b6d3df93fc5aa","schema_version":"1.0","event_id":"sha256:17c90017c7437d83112bb56d3451d977e09994e250dd1a6cdb8b6d3df93fc5aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KUO7VUAM7EHETBRBNKBHVKDN37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections.","cross_cats":["cond-mat.str-el","cs.NA"],"primary_cat":"math.NA","authors_text":"Andreas A. Buchheit, Filipp N. Rybakov, Jonathan K. Busse, Torsten Ke{\\ss}ler","submitted_at":"2025-09-30T13:58:28Z","abstract_excerpt":"We address the efficient computation of power-law-based interaction potentials of homogeneous $d$-dimensional bodies with an infinite $n$-dimensional array of copies, including their higher-order derivatives. This problem forms a serious challenge in micromagnetics with periodic boundary conditions and related fields. Nowadays, it is common practice to truncate the associated infinite lattice sum to a finite number of images, introducing uncontrolled errors. We show that, for general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law po"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law potentials can be obtained by complementing a small direct sum by a correction term that involves efficiently computable derivatives of generalized zeta functions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the required derivatives of generalized zeta functions (and related special functions such as incomplete Bessel functions) admit a superexponentially convergent algorithm that remains practical and stable for the geometries and derivative orders needed in micromagnetics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Zeta-function derivative corrections enable machine-precision evaluation of periodic dipolar and Riesz potentials at the cost of truncated sums.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"238704d15e62520cece48faa75419958e4c70c34a71d9cfc34a45c59e5e6ef5f"},"source":{"id":"2509.26274","kind":"arxiv","version":3},"verdict":{"id":"450a8d96-9bfa-4ae6-8fd9-bf4055ab5cb1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T12:07:34.710621Z","strongest_claim":"For general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law potentials can be obtained by complementing a small direct sum by a correction term that involves efficiently computable derivatives of generalized zeta functions.","one_line_summary":"Zeta-function derivative corrections enable machine-precision evaluation of periodic dipolar and Riesz potentials at the cost of truncated sums.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the required derivatives of generalized zeta functions (and related special functions such as incomplete Bessel functions) admit a superexponentially convergent algorithm that remains practical and stable for the geometries and derivative orders needed in micromagnetics.","pith_extraction_headline":"Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.26274/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":"450a8d96-9bfa-4ae6-8fd9-bf4055ab5cb1"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qz+pvd3e4FjQ2T3/iDWbzodUySX5FZEycBWfn1gnWX88As6D26gWh1BFakgqqXBMxGf7d378ANk+8fQynkDsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:48:28.401052Z"},"content_sha256":"dfca8f2437136a41d7dcc8a2f7212413c3962d5724095813ce166cd28f7d6ee1","schema_version":"1.0","event_id":"sha256:dfca8f2437136a41d7dcc8a2f7212413c3962d5724095813ce166cd28f7d6ee1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUO7VUAM7EHETBRBNKBHVKDN37/bundle.json","state_url":"https://pith.science/pith/KUO7VUAM7EHETBRBNKBHVKDN37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUO7VUAM7EHETBRBNKBHVKDN37/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":"2026-06-20T07:48:28Z","links":{"resolver":"https://pith.science/pith/KUO7VUAM7EHETBRBNKBHVKDN37","bundle":"https://pith.science/pith/KUO7VUAM7EHETBRBNKBHVKDN37/bundle.json","state":"https://pith.science/pith/KUO7VUAM7EHETBRBNKBHVKDN37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUO7VUAM7EHETBRBNKBHVKDN37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KUO7VUAM7EHETBRBNKBHVKDN37","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":"0777cb5ece166b03e15ebf0a192be6951640df0b723214a08b2cd21977fbac2f","cross_cats_sorted":["cond-mat.str-el","cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-30T13:58:28Z","title_canon_sha256":"6aa3cfea5abf1428524d7a6fe27515f933c890ca21ee7b3a0ec66772e2e329a8"},"schema_version":"1.0","source":{"id":"2509.26274","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.26274","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"arxiv_version","alias_value":"2509.26274v3","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.26274","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_12","alias_value":"KUO7VUAM7EHE","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_16","alias_value":"KUO7VUAM7EHETBRB","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_8","alias_value":"KUO7VUAM","created_at":"2026-06-19T16:10:31Z"}],"graph_snapshots":[{"event_id":"sha256:dfca8f2437136a41d7dcc8a2f7212413c3962d5724095813ce166cd28f7d6ee1","target":"graph","created_at":"2026-06-19T16:10:31Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"For general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law potentials can be obtained by complementing a small direct sum by a correction term that involves efficiently computable derivatives of generalized zeta functions."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the required derivatives of generalized zeta functions (and related special functions such as incomplete Bessel functions) admit a superexponentially convergent algorithm that remains practical and stable for the geometries and derivative orders needed in micromagnetics."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Zeta-function derivative corrections enable machine-precision evaluation of periodic dipolar and Riesz potentials at the cost of truncated sums."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections."}],"snapshot_sha256":"238704d15e62520cece48faa75419958e4c70c34a71d9cfc34a45c59e5e6ef5f"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.26274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the efficient computation of power-law-based interaction potentials of homogeneous $d$-dimensional bodies with an infinite $n$-dimensional array of copies, including their higher-order derivatives. This problem forms a serious challenge in micromagnetics with periodic boundary conditions and related fields. Nowadays, it is common practice to truncate the associated infinite lattice sum to a finite number of images, introducing uncontrolled errors. We show that, for general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law po","authors_text":"Andreas A. Buchheit, Filipp N. Rybakov, Jonathan K. Busse, Torsten Ke{\\ss}ler","cross_cats":["cond-mat.str-el","cs.NA"],"headline":"Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-30T13:58:28Z","title":"Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.26274","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-18T12:07:34.710621Z","id":"450a8d96-9bfa-4ae6-8fd9-bf4055ab5cb1","model_set":{"reader":"grok-4.3"},"one_line_summary":"Zeta-function derivative corrections enable machine-precision evaluation of periodic dipolar and Riesz potentials at the cost of truncated sums.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections.","strongest_claim":"For general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law potentials can be obtained by complementing a small direct sum by a correction term that involves efficiently computable derivatives of generalized zeta functions.","weakest_assumption":"That the required derivatives of generalized zeta functions (and related special functions such as incomplete Bessel functions) admit a superexponentially convergent algorithm that remains practical and stable for the geometries and derivative orders needed in micromagnetics."}},"verdict_id":"450a8d96-9bfa-4ae6-8fd9-bf4055ab5cb1"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:17c90017c7437d83112bb56d3451d977e09994e250dd1a6cdb8b6d3df93fc5aa","target":"record","created_at":"2026-06-19T16:10:31Z","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":"0777cb5ece166b03e15ebf0a192be6951640df0b723214a08b2cd21977fbac2f","cross_cats_sorted":["cond-mat.str-el","cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-30T13:58:28Z","title_canon_sha256":"6aa3cfea5abf1428524d7a6fe27515f933c890ca21ee7b3a0ec66772e2e329a8"},"schema_version":"1.0","source":{"id":"2509.26274","kind":"arxiv","version":3}},"canonical_sha256":"551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126","first_computed_at":"2026-06-19T16:10:31.462326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:31.462326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EBLVwogGtSAKAIXWCZosibW2tkrvlh7GJLIL5ObTd5EzQAxG3FZa9X/uruoGMIdnOfhmJ9Y3ZE3mdJ6wZIpWDg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:31.462776Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.26274","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17c90017c7437d83112bb56d3451d977e09994e250dd1a6cdb8b6d3df93fc5aa","sha256:dfca8f2437136a41d7dcc8a2f7212413c3962d5724095813ce166cd28f7d6ee1"],"state_sha256":"bbe571a41026a6e14b1358bce391133ce424913896fbdee9f2e8e643acf56480"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDktAQhF7z26cjN//Qxfj3alq3K/gonO9y1yUf4fnzkU2QoQP1GJYvo0YsuMA50ugWkLzb3yImQUHUk1OsMGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:48:28.403306Z","bundle_sha256":"ef7a08c637e78af8a5f06786924ca0863f2de2dcd68e616bb63c39fbd6f8bc20"}}