{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BRZ5VF5DVRE57QEOW27JE5IMFX","short_pith_number":"pith:BRZ5VF5D","canonical_record":{"source":{"id":"1804.07281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-19T17:29:10Z","cross_cats_sorted":[],"title_canon_sha256":"658d105f3e821c2224e88473c28865ddeddbd1b58c0eba0e23e2c98a71871552","abstract_canon_sha256":"f1a07e13a49e6c0d5d7bf7c1d29c3f2ef3b552d2b3dd2751e8f685c64bcb4129"},"schema_version":"1.0"},"canonical_sha256":"0c73da97a3ac49dfc08eb6be92750c2dc7459268fc63fe39ae58a8c76d541b8e","source":{"kind":"arxiv","id":"1804.07281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07281","created_at":"2026-05-18T00:18:00Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07281v1","created_at":"2026-05-18T00:18:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07281","created_at":"2026-05-18T00:18:00Z"},{"alias_kind":"pith_short_12","alias_value":"BRZ5VF5DVRE5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BRZ5VF5DVRE57QEO","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BRZ5VF5D","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BRZ5VF5DVRE57QEOW27JE5IMFX","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-19T17:29:10Z","cross_cats_sorted":[],"title_canon_sha256":"658d105f3e821c2224e88473c28865ddeddbd1b58c0eba0e23e2c98a71871552","abstract_canon_sha256":"f1a07e13a49e6c0d5d7bf7c1d29c3f2ef3b552d2b3dd2751e8f685c64bcb4129"},"schema_version":"1.0"},"canonical_sha256":"0c73da97a3ac49dfc08eb6be92750c2dc7459268fc63fe39ae58a8c76d541b8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:00.766591Z","signature_b64":"EkUmwakFS0Yt9nz2Cs1z4IMa0gZ7jde0R6rfWRceQGBm20DeeGNWnn75Rn8faGRM2uJmuZFl2H7gjuZXbTUmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c73da97a3ac49dfc08eb6be92750c2dc7459268fc63fe39ae58a8c76d541b8e","last_reissued_at":"2026-05-18T00:18:00.765793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:00.765793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07281","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":"2026-05-18T00:18:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tifsVKVOU0Vump7FLxSIhqVtOmeVXeHVhdKzP7aCWd7+hL8bPHKePBZFfEH6nFZH3vuy8SmE1uBsCw53deB/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:03:28.823973Z"},"content_sha256":"82f606afb9dde5c96f629730db9a402da05c29969dcad608c305770e422ed8e7","schema_version":"1.0","event_id":"sha256:82f606afb9dde5c96f629730db9a402da05c29969dcad608c305770e422ed8e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BRZ5VF5DVRE57QEOW27JE5IMFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditionally complete sponges: new results on generalized lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jasper J. van de Gronde, Wim H. Hesselink","submitted_at":"2018-04-19T17:29:10Z","abstract_excerpt":"Sponges were recently proposed as a generalization of lattices, focussing on joins/meets of sets, while letting go of associativity/transitivity. In this work we provide tools for characterizing and constructing sponges on metric spaces and groups. These are then used in a characterization of epigraph sponges: a new class of sponges on Hilbert spaces whose sets of left/right bounds are formed by the epigraph of a rotationally symmetric function. We also show that the so-called hyperbolic sponge generalizes to more than two dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07281","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":"2026-05-18T00:18:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jhqyw5x9Z7W3js7PnKteJPApCo2MBPyc1uXVDL0LWFDG8XU1Z7/CP7q9yB0M/zTssug5gEcL3qs7GERpnklnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:03:28.824719Z"},"content_sha256":"aaa8889ecf4bbeaad5950be0940bd5c56d6ea76463abb31d1e86a9c5d611bd94","schema_version":"1.0","event_id":"sha256:aaa8889ecf4bbeaad5950be0940bd5c56d6ea76463abb31d1e86a9c5d611bd94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRZ5VF5DVRE57QEOW27JE5IMFX/bundle.json","state_url":"https://pith.science/pith/BRZ5VF5DVRE57QEOW27JE5IMFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRZ5VF5DVRE57QEOW27JE5IMFX/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":"2026-06-08T08:03:28Z","links":{"resolver":"https://pith.science/pith/BRZ5VF5DVRE57QEOW27JE5IMFX","bundle":"https://pith.science/pith/BRZ5VF5DVRE57QEOW27JE5IMFX/bundle.json","state":"https://pith.science/pith/BRZ5VF5DVRE57QEOW27JE5IMFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRZ5VF5DVRE57QEOW27JE5IMFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BRZ5VF5DVRE57QEOW27JE5IMFX","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":"f1a07e13a49e6c0d5d7bf7c1d29c3f2ef3b552d2b3dd2751e8f685c64bcb4129","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-19T17:29:10Z","title_canon_sha256":"658d105f3e821c2224e88473c28865ddeddbd1b58c0eba0e23e2c98a71871552"},"schema_version":"1.0","source":{"id":"1804.07281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07281","created_at":"2026-05-18T00:18:00Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07281v1","created_at":"2026-05-18T00:18:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07281","created_at":"2026-05-18T00:18:00Z"},{"alias_kind":"pith_short_12","alias_value":"BRZ5VF5DVRE5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BRZ5VF5DVRE57QEO","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BRZ5VF5D","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:aaa8889ecf4bbeaad5950be0940bd5c56d6ea76463abb31d1e86a9c5d611bd94","target":"graph","created_at":"2026-05-18T00:18:00Z","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":"Sponges were recently proposed as a generalization of lattices, focussing on joins/meets of sets, while letting go of associativity/transitivity. In this work we provide tools for characterizing and constructing sponges on metric spaces and groups. These are then used in a characterization of epigraph sponges: a new class of sponges on Hilbert spaces whose sets of left/right bounds are formed by the epigraph of a rotationally symmetric function. We also show that the so-called hyperbolic sponge generalizes to more than two dimensions.","authors_text":"Jasper J. van de Gronde, Wim H. Hesselink","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-19T17:29:10Z","title":"Conditionally complete sponges: new results on generalized lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07281","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":"sha256:82f606afb9dde5c96f629730db9a402da05c29969dcad608c305770e422ed8e7","target":"record","created_at":"2026-05-18T00:18:00Z","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":"f1a07e13a49e6c0d5d7bf7c1d29c3f2ef3b552d2b3dd2751e8f685c64bcb4129","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-19T17:29:10Z","title_canon_sha256":"658d105f3e821c2224e88473c28865ddeddbd1b58c0eba0e23e2c98a71871552"},"schema_version":"1.0","source":{"id":"1804.07281","kind":"arxiv","version":1}},"canonical_sha256":"0c73da97a3ac49dfc08eb6be92750c2dc7459268fc63fe39ae58a8c76d541b8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c73da97a3ac49dfc08eb6be92750c2dc7459268fc63fe39ae58a8c76d541b8e","first_computed_at":"2026-05-18T00:18:00.765793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:00.765793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EkUmwakFS0Yt9nz2Cs1z4IMa0gZ7jde0R6rfWRceQGBm20DeeGNWnn75Rn8faGRM2uJmuZFl2H7gjuZXbTUmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:00.766591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f606afb9dde5c96f629730db9a402da05c29969dcad608c305770e422ed8e7","sha256:aaa8889ecf4bbeaad5950be0940bd5c56d6ea76463abb31d1e86a9c5d611bd94"],"state_sha256":"501046e6ce331e5bf421c419fb0d78d3a6d1ee1cef8d331e38db105d2f0155c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pEJ+6pIhrdTP6n0T8MVw1S4nmkbMPu2knbIJEh5ybmOU3SZces90xJZ4UJnBjdssPXLlt+I52uxWbl626XVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T08:03:28.828674Z","bundle_sha256":"c319ec92413bed53ea011c8815dcb389ecc436c44e12c33bf8005a50924ab21c"}}