{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BUORR5DHHTNKC5N3T3JWNGQSMN","short_pith_number":"pith:BUORR5DH","canonical_record":{"source":{"id":"1002.2103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-10T14:54:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3486e82a802e68c9d103b3a320ee898212ab9491804031e6a73dea4da2a36168","abstract_canon_sha256":"d81c9fe9f0d6230feb47e63bae095e81f72c1877ac78ed927f5891fb56328d65"},"schema_version":"1.0"},"canonical_sha256":"0d1d18f4673cdaa175bb9ed3669a126377779627c1e3b7e91999c02928f032f2","source":{"kind":"arxiv","id":"1002.2103","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2103","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2103v2","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2103","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"BUORR5DHHTNK","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BUORR5DHHTNKC5N3","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BUORR5DH","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BUORR5DHHTNKC5N3T3JWNGQSMN","target":"record","payload":{"canonical_record":{"source":{"id":"1002.2103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-10T14:54:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3486e82a802e68c9d103b3a320ee898212ab9491804031e6a73dea4da2a36168","abstract_canon_sha256":"d81c9fe9f0d6230feb47e63bae095e81f72c1877ac78ed927f5891fb56328d65"},"schema_version":"1.0"},"canonical_sha256":"0d1d18f4673cdaa175bb9ed3669a126377779627c1e3b7e91999c02928f032f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:05.482068Z","signature_b64":"zn4eay9bcweFQj4D+FDaCD+MdqAGr2j4+b14MuAmwjDvWEMpLiuxC5grhSJA54kIa91e1EBAafGyld3jL7mhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d1d18f4673cdaa175bb9ed3669a126377779627c1e3b7e91999c02928f032f2","last_reissued_at":"2026-05-18T03:43:05.481446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:05.481446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.2103","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":"2026-05-18T03:43:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QQHvsV57yuVOcL0jiUNWSB3QFrpirD7Tbz2q9FivIzilncTGm/e4ENYYSZM/+imZ2vCn8m1TXCVjxhZLjehjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:40:26.453247Z"},"content_sha256":"d2b150044d30168892673cada12a6b312c4b800b5f9982c1b21650ef462d9b44","schema_version":"1.0","event_id":"sha256:d2b150044d30168892673cada12a6b312c4b800b5f9982c1b21650ef462d9b44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BUORR5DHHTNKC5N3T3JWNGQSMN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifshitz tails for a percolation model in the continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hatem Najar, Werner Kirsch","submitted_at":"2010-02-10T14:54:25Z","abstract_excerpt":"In this paper we study Lifshitz tails for continuous Laplacian in a continuous site percolation situation. By this we mean that we delete a random set $\\Gamma_\\omega$ from $IR^d$ and consider the Dirichlet or Neumann Laplacian on $D=IR^d\\setminus\\Gamma_\\omega$. We prove that the integrated density of states exhibits Lifshitz behavior at the bottom of the spectrum when we consider Dirichlet boundary conditions, while when we consider Neumann boundary conditions, it is bounded from below by a van Hove behavior. The Lifshitz tails are proven independently of the percolation probability, whereas f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2103","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":"2026-05-18T03:43:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ag0+sxQU09fuUVpbjmhEnuHEqX25nL+JwhRwRblIwt+yxK2CFhzuLOgMG8C/aMLwj4e+YddIqnyqRLX5bryBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:40:26.453612Z"},"content_sha256":"86a8460323d8d9fe66d89baf6d4c76f45d4ef8f4940d68c4749cee3aa20e0fcf","schema_version":"1.0","event_id":"sha256:86a8460323d8d9fe66d89baf6d4c76f45d4ef8f4940d68c4749cee3aa20e0fcf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUORR5DHHTNKC5N3T3JWNGQSMN/bundle.json","state_url":"https://pith.science/pith/BUORR5DHHTNKC5N3T3JWNGQSMN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUORR5DHHTNKC5N3T3JWNGQSMN/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":"2026-06-04T21:40:26Z","links":{"resolver":"https://pith.science/pith/BUORR5DHHTNKC5N3T3JWNGQSMN","bundle":"https://pith.science/pith/BUORR5DHHTNKC5N3T3JWNGQSMN/bundle.json","state":"https://pith.science/pith/BUORR5DHHTNKC5N3T3JWNGQSMN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUORR5DHHTNKC5N3T3JWNGQSMN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BUORR5DHHTNKC5N3T3JWNGQSMN","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":"d81c9fe9f0d6230feb47e63bae095e81f72c1877ac78ed927f5891fb56328d65","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-10T14:54:25Z","title_canon_sha256":"3486e82a802e68c9d103b3a320ee898212ab9491804031e6a73dea4da2a36168"},"schema_version":"1.0","source":{"id":"1002.2103","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.2103","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"1002.2103v2","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.2103","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"BUORR5DHHTNK","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BUORR5DHHTNKC5N3","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BUORR5DH","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:86a8460323d8d9fe66d89baf6d4c76f45d4ef8f4940d68c4749cee3aa20e0fcf","target":"graph","created_at":"2026-05-18T03:43:05Z","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":"In this paper we study Lifshitz tails for continuous Laplacian in a continuous site percolation situation. By this we mean that we delete a random set $\\Gamma_\\omega$ from $IR^d$ and consider the Dirichlet or Neumann Laplacian on $D=IR^d\\setminus\\Gamma_\\omega$. We prove that the integrated density of states exhibits Lifshitz behavior at the bottom of the spectrum when we consider Dirichlet boundary conditions, while when we consider Neumann boundary conditions, it is bounded from below by a van Hove behavior. The Lifshitz tails are proven independently of the percolation probability, whereas f","authors_text":"Hatem Najar, Werner Kirsch","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-10T14:54:25Z","title":"Lifshitz tails for a percolation model in the continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2103","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:d2b150044d30168892673cada12a6b312c4b800b5f9982c1b21650ef462d9b44","target":"record","created_at":"2026-05-18T03:43:05Z","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":"d81c9fe9f0d6230feb47e63bae095e81f72c1877ac78ed927f5891fb56328d65","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-10T14:54:25Z","title_canon_sha256":"3486e82a802e68c9d103b3a320ee898212ab9491804031e6a73dea4da2a36168"},"schema_version":"1.0","source":{"id":"1002.2103","kind":"arxiv","version":2}},"canonical_sha256":"0d1d18f4673cdaa175bb9ed3669a126377779627c1e3b7e91999c02928f032f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d1d18f4673cdaa175bb9ed3669a126377779627c1e3b7e91999c02928f032f2","first_computed_at":"2026-05-18T03:43:05.481446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:05.481446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zn4eay9bcweFQj4D+FDaCD+MdqAGr2j4+b14MuAmwjDvWEMpLiuxC5grhSJA54kIa91e1EBAafGyld3jL7mhBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:05.482068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.2103","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2b150044d30168892673cada12a6b312c4b800b5f9982c1b21650ef462d9b44","sha256:86a8460323d8d9fe66d89baf6d4c76f45d4ef8f4940d68c4749cee3aa20e0fcf"],"state_sha256":"1ee95397fee2f280e97802904371d3ce7a2603b6e639b8837f315308182f5a77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgAeR3aBlOzj7lNYx6yrgTK4XoDqLVkGnCyrt1K4MfAbw8iJKYUNzYHzv1uNO6ljeumxg2WSnnTV+EBoaSKOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:40:26.455610Z","bundle_sha256":"88eba75bfe6de8399d9bdf7b254f19d7beabbe88e2df84193c7ab44b627db5b6"}}