{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BWAEAZXYPWVDZT272R43MUX64L","short_pith_number":"pith:BWAEAZXY","canonical_record":{"source":{"id":"1312.5454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-19T09:24:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b6a4ddd0bc5e9455d4478d356a77f14622168f18c6937a0cc20fa6de43c5d2ac","abstract_canon_sha256":"4e9d3ee4d0285d4ce25a4b7b19704bd4fe89f17734ec5745b9b72a44177fe78b"},"schema_version":"1.0"},"canonical_sha256":"0d804066f87daa3ccf5fd479b652fee2ce2e0a55f8cc16d63452f43c86ebc0a5","source":{"kind":"arxiv","id":"1312.5454","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5454","created_at":"2026-05-18T01:45:44Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5454v1","created_at":"2026-05-18T01:45:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5454","created_at":"2026-05-18T01:45:44Z"},{"alias_kind":"pith_short_12","alias_value":"BWAEAZXYPWVD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BWAEAZXYPWVDZT27","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BWAEAZXY","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BWAEAZXYPWVDZT272R43MUX64L","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5454","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-19T09:24:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b6a4ddd0bc5e9455d4478d356a77f14622168f18c6937a0cc20fa6de43c5d2ac","abstract_canon_sha256":"4e9d3ee4d0285d4ce25a4b7b19704bd4fe89f17734ec5745b9b72a44177fe78b"},"schema_version":"1.0"},"canonical_sha256":"0d804066f87daa3ccf5fd479b652fee2ce2e0a55f8cc16d63452f43c86ebc0a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:44.110577Z","signature_b64":"ALLmvxcE9MTU4MGCYFhPHyeHi1dUlN80uO+VEK9KGxOJhD+qkWZueEwOHRP7wcG+vJJke98VoNJdwX9e0pInCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d804066f87daa3ccf5fd479b652fee2ce2e0a55f8cc16d63452f43c86ebc0a5","last_reissued_at":"2026-05-18T01:45:44.109799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:44.109799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5454","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":"2026-05-18T01:45:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"erYQCS9YRylAlpO0xN145vCkkKyAhXExfYK3dxKc6bSEOKVMoVr70p9s6EPX3L8GnvvvAz0sh3zQYhbilXZvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:25:55.488253Z"},"content_sha256":"09c5185c9f3c81786de221df0139ab508aa6990b468fb21cd5a627c9fa436334","schema_version":"1.0","event_id":"sha256:09c5185c9f3c81786de221df0139ab508aa6990b468fb21cd5a627c9fa436334"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BWAEAZXYPWVDZT272R43MUX64L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudo-Riemannian geometry in terms of multi-linear brackets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Gerhard Huisken, Joakim Arnlind","submitted_at":"2013-12-19T09:24:05Z","abstract_excerpt":"We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)K\\\"ahler geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5454","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":"2026-05-18T01:45:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0a/Y9+l6R5gG+4/26B6idP1CcZdNwPL8lR1/BKeFb9yRFZsSTqvvf1ZO5ZRt8lIIxJLgaAoxQ76cbnfFnOjpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:25:55.488607Z"},"content_sha256":"50bbfa669e1f23cb0c0a177045cbc821b9392521c30cad8038221fdcff604673","schema_version":"1.0","event_id":"sha256:50bbfa669e1f23cb0c0a177045cbc821b9392521c30cad8038221fdcff604673"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWAEAZXYPWVDZT272R43MUX64L/bundle.json","state_url":"https://pith.science/pith/BWAEAZXYPWVDZT272R43MUX64L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWAEAZXYPWVDZT272R43MUX64L/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":"2026-06-01T08:25:55Z","links":{"resolver":"https://pith.science/pith/BWAEAZXYPWVDZT272R43MUX64L","bundle":"https://pith.science/pith/BWAEAZXYPWVDZT272R43MUX64L/bundle.json","state":"https://pith.science/pith/BWAEAZXYPWVDZT272R43MUX64L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWAEAZXYPWVDZT272R43MUX64L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BWAEAZXYPWVDZT272R43MUX64L","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":"4e9d3ee4d0285d4ce25a4b7b19704bd4fe89f17734ec5745b9b72a44177fe78b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-19T09:24:05Z","title_canon_sha256":"b6a4ddd0bc5e9455d4478d356a77f14622168f18c6937a0cc20fa6de43c5d2ac"},"schema_version":"1.0","source":{"id":"1312.5454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5454","created_at":"2026-05-18T01:45:44Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5454v1","created_at":"2026-05-18T01:45:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5454","created_at":"2026-05-18T01:45:44Z"},{"alias_kind":"pith_short_12","alias_value":"BWAEAZXYPWVD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BWAEAZXYPWVDZT27","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BWAEAZXY","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:50bbfa669e1f23cb0c0a177045cbc821b9392521c30cad8038221fdcff604673","target":"graph","created_at":"2026-05-18T01:45:44Z","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 show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)K\\\"ahler geometry.","authors_text":"Gerhard Huisken, Joakim Arnlind","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-19T09:24:05Z","title":"Pseudo-Riemannian geometry in terms of multi-linear brackets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5454","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":"sha256:09c5185c9f3c81786de221df0139ab508aa6990b468fb21cd5a627c9fa436334","target":"record","created_at":"2026-05-18T01:45:44Z","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":"4e9d3ee4d0285d4ce25a4b7b19704bd4fe89f17734ec5745b9b72a44177fe78b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-19T09:24:05Z","title_canon_sha256":"b6a4ddd0bc5e9455d4478d356a77f14622168f18c6937a0cc20fa6de43c5d2ac"},"schema_version":"1.0","source":{"id":"1312.5454","kind":"arxiv","version":1}},"canonical_sha256":"0d804066f87daa3ccf5fd479b652fee2ce2e0a55f8cc16d63452f43c86ebc0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d804066f87daa3ccf5fd479b652fee2ce2e0a55f8cc16d63452f43c86ebc0a5","first_computed_at":"2026-05-18T01:45:44.109799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:44.109799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ALLmvxcE9MTU4MGCYFhPHyeHi1dUlN80uO+VEK9KGxOJhD+qkWZueEwOHRP7wcG+vJJke98VoNJdwX9e0pInCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:44.110577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09c5185c9f3c81786de221df0139ab508aa6990b468fb21cd5a627c9fa436334","sha256:50bbfa669e1f23cb0c0a177045cbc821b9392521c30cad8038221fdcff604673"],"state_sha256":"621d827e76eb8f798bb75a155cc27c27d8dcccb882f40f3c2ef68223df817df5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O70Y/m5iW9i5EePnZhnojAHg7iI3YSYJMapfY4l4vmao6dYhJR97FolKOo/Hk3AKb1G9zmx3hN0SYUT7S8OTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:25:55.490475Z","bundle_sha256":"3d70afc7f09f7ec9c34664353af1e246be01a53a8c28d8f24f56786b059b5eaf"}}