{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BZFHCBR33EAP44V6DBH6UFCGK7","short_pith_number":"pith:BZFHCBR3","canonical_record":{"source":{"id":"1904.06889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T07:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"188719fbb9f66e704cad7bdb78a22e851cececa05cde43ce5bcceaec85a18cad","abstract_canon_sha256":"b9b389cb7521533b78826a2d0618fd065302a7abd73d0ee1d24947e484e9f823"},"schema_version":"1.0"},"canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","source":{"kind":"arxiv","id":"1904.06889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06889","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06889v1","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06889","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"BZFHCBR33EAP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BZFHCBR33EAP44V6","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BZFHCBR3","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BZFHCBR33EAP44V6DBH6UFCGK7","target":"record","payload":{"canonical_record":{"source":{"id":"1904.06889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T07:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"188719fbb9f66e704cad7bdb78a22e851cececa05cde43ce5bcceaec85a18cad","abstract_canon_sha256":"b9b389cb7521533b78826a2d0618fd065302a7abd73d0ee1d24947e484e9f823"},"schema_version":"1.0"},"canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:35.869601Z","signature_b64":"Jn2M8HfxO6jdO2u+DvpFQCwJOztYJS5srT1AB3ZY3OmiCR3aMm0xS6ykI5gptS1dxXfHFrSrV9w+QgBwXoYyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","last_reissued_at":"2026-05-17T23:48:35.868865Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:35.868865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.06889","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":"2026-05-17T23:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k387kg2EemANsDvJZipolOrTD7TzTE1C3ggrAZuW0n74yND+8nZ2I9cK7uEWSrm0BpfFL4cXZSOvmfMqOR2xAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:16:03.495529Z"},"content_sha256":"f019a5cc45a13258a652dd0df86ce9f01c9cd5ee5751af8c3d59700773c54cbe","schema_version":"1.0","event_id":"sha256:f019a5cc45a13258a652dd0df86ce9f01c9cd5ee5751af8c3d59700773c54cbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BZFHCBR33EAP44V6DBH6UFCGK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Franziska Flegel, Martin Heida","submitted_at":"2019-04-15T07:44:47Z","abstract_excerpt":"We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator.\n  Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06889","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":"2026-05-17T23:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pinWN10JMLgWfjHc42QmAoSjA7KthR2QfCb8LYmnCd7m/ciIV8AODxXaHjWuUx17DiQP6wCGO7j6721cLU7BDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:16:03.495884Z"},"content_sha256":"41c8ef90f52e4cc0f7974516dd275e17669964bcdc17343eb9df0eb486a0c5c4","schema_version":"1.0","event_id":"sha256:41c8ef90f52e4cc0f7974516dd275e17669964bcdc17343eb9df0eb486a0c5c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/bundle.json","state_url":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BZFHCBR33EAP44V6DBH6UFCGK7/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":"2026-05-27T20:16:03Z","links":{"resolver":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7","bundle":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/bundle.json","state":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BZFHCBR33EAP44V6DBH6UFCGK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BZFHCBR33EAP44V6DBH6UFCGK7","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":"b9b389cb7521533b78826a2d0618fd065302a7abd73d0ee1d24947e484e9f823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T07:44:47Z","title_canon_sha256":"188719fbb9f66e704cad7bdb78a22e851cececa05cde43ce5bcceaec85a18cad"},"schema_version":"1.0","source":{"id":"1904.06889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06889","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06889v1","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06889","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"BZFHCBR33EAP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BZFHCBR33EAP44V6","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BZFHCBR3","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:41c8ef90f52e4cc0f7974516dd275e17669964bcdc17343eb9df0eb486a0c5c4","target":"graph","created_at":"2026-05-17T23:48:35Z","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 study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator.\n  Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator.","authors_text":"Franziska Flegel, Martin Heida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T07:44:47Z","title":"The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06889","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:f019a5cc45a13258a652dd0df86ce9f01c9cd5ee5751af8c3d59700773c54cbe","target":"record","created_at":"2026-05-17T23:48:35Z","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":"b9b389cb7521533b78826a2d0618fd065302a7abd73d0ee1d24947e484e9f823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T07:44:47Z","title_canon_sha256":"188719fbb9f66e704cad7bdb78a22e851cececa05cde43ce5bcceaec85a18cad"},"schema_version":"1.0","source":{"id":"1904.06889","kind":"arxiv","version":1}},"canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","first_computed_at":"2026-05-17T23:48:35.868865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:35.868865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jn2M8HfxO6jdO2u+DvpFQCwJOztYJS5srT1AB3ZY3OmiCR3aMm0xS6ykI5gptS1dxXfHFrSrV9w+QgBwXoYyAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:35.869601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f019a5cc45a13258a652dd0df86ce9f01c9cd5ee5751af8c3d59700773c54cbe","sha256:41c8ef90f52e4cc0f7974516dd275e17669964bcdc17343eb9df0eb486a0c5c4"],"state_sha256":"199f63be567bf0a5ccff0211e5ec96f2d097b0e63f68968c22a460fc07bfbadb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pd9yIf8MHKyNfKMbMp6JTztr5+71aFCHh5kdCqDhtmW1QjMdg27060KYfOt24KSBADvDNdKlWcbC9NZUoFWbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:16:03.498643Z","bundle_sha256":"1fa924ed43c7e3b90bc1b043a4d88ce216c7d8729de3ccddc2d2fc5b4fda9ae9"}}