{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4UQMA7LDX4VDGLACZF2MCBKJ4Z","short_pith_number":"pith:4UQMA7LD","canonical_record":{"source":{"id":"1501.01393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-07T08:43:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3e582f0abb3dcdf093f1c46367e75fa30d012e45b6ed92f9de611954bbb153e6","abstract_canon_sha256":"4970ca15234b9ed3ca708631f47072857050ab92ed01aa52fd86270013fba81a"},"schema_version":"1.0"},"canonical_sha256":"e520c07d63bf2a332c02c974c10549e64dd5bb1504c8d076d9f296b71ded062c","source":{"kind":"arxiv","id":"1501.01393","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01393","created_at":"2026-05-18T01:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01393v1","created_at":"2026-05-18T01:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01393","created_at":"2026-05-18T01:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"4UQMA7LDX4VD","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4UQMA7LDX4VDGLAC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4UQMA7LD","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4UQMA7LDX4VDGLACZF2MCBKJ4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-07T08:43:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3e582f0abb3dcdf093f1c46367e75fa30d012e45b6ed92f9de611954bbb153e6","abstract_canon_sha256":"4970ca15234b9ed3ca708631f47072857050ab92ed01aa52fd86270013fba81a"},"schema_version":"1.0"},"canonical_sha256":"e520c07d63bf2a332c02c974c10549e64dd5bb1504c8d076d9f296b71ded062c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:14.117792Z","signature_b64":"VNin6p02e2zd3lQgA/0N8wm30ziMnPPy9ZKWXG2OHkialYnPxTCyjwlfJOBgOtEcO8ZH9tMlkDjhcq3jnaq/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e520c07d63bf2a332c02c974c10549e64dd5bb1504c8d076d9f296b71ded062c","last_reissued_at":"2026-05-18T01:41:14.117282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:14.117282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01393","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":"2026-05-18T01:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MW7cmAtti/W/wDB8Gw1epSAdF3CR9LPLWGoGwu0VhbyzYFwbv0ldpiR0lBNoSiExcxsyANcUR+i2QaFLptuuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:57:45.348877Z"},"content_sha256":"d1c631d430c3cb0f5abd3d0504f037e30c832e3619341345a7539baac5381470","schema_version":"1.0","event_id":"sha256:d1c631d430c3cb0f5abd3d0504f037e30c832e3619341345a7539baac5381470"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4UQMA7LDX4VDGLACZF2MCBKJ4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac lattices, zero-range potentials and self adjoint extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J.M. Munoz-Castaneda, M. Bordag","submitted_at":"2015-01-07T08:43:49Z","abstract_excerpt":"We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the selfadjoint extension, regularization/renormalisation and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01393","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":"2026-05-18T01:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XRisid65B9BoHWrzbWkKf5cu7KJAcHSZVRQQC+PRQXqdDVZQRHwPDIQZEj78BkWcyAHsspdxOxkxaIu1dfxXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:57:45.349290Z"},"content_sha256":"c39c447cf2058086c8f51c5adedf356e8e65eb53e2a68bc2161aaae3eda8beee","schema_version":"1.0","event_id":"sha256:c39c447cf2058086c8f51c5adedf356e8e65eb53e2a68bc2161aaae3eda8beee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z/bundle.json","state_url":"https://pith.science/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z/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":"2026-05-25T17:57:45Z","links":{"resolver":"https://pith.science/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z","bundle":"https://pith.science/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z/bundle.json","state":"https://pith.science/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4UQMA7LDX4VDGLACZF2MCBKJ4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4UQMA7LDX4VDGLACZF2MCBKJ4Z","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":"4970ca15234b9ed3ca708631f47072857050ab92ed01aa52fd86270013fba81a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-07T08:43:49Z","title_canon_sha256":"3e582f0abb3dcdf093f1c46367e75fa30d012e45b6ed92f9de611954bbb153e6"},"schema_version":"1.0","source":{"id":"1501.01393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01393","created_at":"2026-05-18T01:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01393v1","created_at":"2026-05-18T01:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01393","created_at":"2026-05-18T01:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"4UQMA7LDX4VD","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4UQMA7LDX4VDGLAC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4UQMA7LD","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:c39c447cf2058086c8f51c5adedf356e8e65eb53e2a68bc2161aaae3eda8beee","target":"graph","created_at":"2026-05-18T01:41:14Z","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 consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the selfadjoint extension, regularization/renormalisation and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for","authors_text":"J.M. Munoz-Castaneda, M. Bordag","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-07T08:43:49Z","title":"Dirac lattices, zero-range potentials and self adjoint extension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01393","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:d1c631d430c3cb0f5abd3d0504f037e30c832e3619341345a7539baac5381470","target":"record","created_at":"2026-05-18T01:41:14Z","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":"4970ca15234b9ed3ca708631f47072857050ab92ed01aa52fd86270013fba81a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-07T08:43:49Z","title_canon_sha256":"3e582f0abb3dcdf093f1c46367e75fa30d012e45b6ed92f9de611954bbb153e6"},"schema_version":"1.0","source":{"id":"1501.01393","kind":"arxiv","version":1}},"canonical_sha256":"e520c07d63bf2a332c02c974c10549e64dd5bb1504c8d076d9f296b71ded062c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e520c07d63bf2a332c02c974c10549e64dd5bb1504c8d076d9f296b71ded062c","first_computed_at":"2026-05-18T01:41:14.117282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:14.117282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VNin6p02e2zd3lQgA/0N8wm30ziMnPPy9ZKWXG2OHkialYnPxTCyjwlfJOBgOtEcO8ZH9tMlkDjhcq3jnaq/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:14.117792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1c631d430c3cb0f5abd3d0504f037e30c832e3619341345a7539baac5381470","sha256:c39c447cf2058086c8f51c5adedf356e8e65eb53e2a68bc2161aaae3eda8beee"],"state_sha256":"561638e2e83ad55d5c18130ae6d0db3a057342a552224b610d78a1bd3fb4b282"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yIyJ9yaPO3AuIttjzuhgDHKn6MQOBt1vV4c3jqyouWgxVY8Jnb55dGbuw6v+v+fM4pIYOnJdzC29RMmpVlgkBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:57:45.352720Z","bundle_sha256":"d8f29c68309ea7032f3c527cd2302b6c70188efc3064d8353d9c35ff03155fe5"}}