{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GJZA6BKDG3HM5FWDVWTDJVLTRE","short_pith_number":"pith:GJZA6BKD","canonical_record":{"source":{"id":"1611.02487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-08T11:51:06Z","cross_cats_sorted":[],"title_canon_sha256":"8937d967870a4a2982c2b876e20bf4e1500f1fc56a703d5922b597714c8f2a08","abstract_canon_sha256":"488d41b30dee56d4281dc85444b3c8d6d5f3befea3eb97448ba0ccb755b2d092"},"schema_version":"1.0"},"canonical_sha256":"32720f054336cece96c3ada634d57389343f4dabb9ffd66e52a7ce8373a8355c","source":{"kind":"arxiv","id":"1611.02487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02487","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02487v1","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02487","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"pith_short_12","alias_value":"GJZA6BKDG3HM","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GJZA6BKDG3HM5FWD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GJZA6BKD","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GJZA6BKDG3HM5FWDVWTDJVLTRE","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-08T11:51:06Z","cross_cats_sorted":[],"title_canon_sha256":"8937d967870a4a2982c2b876e20bf4e1500f1fc56a703d5922b597714c8f2a08","abstract_canon_sha256":"488d41b30dee56d4281dc85444b3c8d6d5f3befea3eb97448ba0ccb755b2d092"},"schema_version":"1.0"},"canonical_sha256":"32720f054336cece96c3ada634d57389343f4dabb9ffd66e52a7ce8373a8355c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:51.894022Z","signature_b64":"rj4j/1/SkovkTsqklJpbR9m0VF6FgZMe/s/1G6ONEVvpa5HuGUGjrtcpB/Bus6TcGHXeOmrHfbW7lkzwRuGJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32720f054336cece96c3ada634d57389343f4dabb9ffd66e52a7ce8373a8355c","last_reissued_at":"2026-05-18T00:59:51.893282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:51.893282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02487","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":"2026-05-18T00:59:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5C3rX8BMbrg3RQt4AxvXXbL0txZD5kYpIGhuYcKMnpuIgqH0colWssPeK8oZrl7iao7dOyQKVfpuB6hmlPJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:49:03.097903Z"},"content_sha256":"e06d1b28c2a57fbb0dd7b712b0849839aff0c7d4bb14ec5c5e95b8d328de4812","schema_version":"1.0","event_id":"sha256:e06d1b28c2a57fbb0dd7b712b0849839aff0c7d4bb14ec5c5e95b8d328de4812"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GJZA6BKDG3HM5FWDVWTDJVLTRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed points of Hammerstein-type equations on general cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"F. Adri\\'an F. Tojo, Rub\\'en Figueroa","submitted_at":"2016-11-08T11:51:06Z","abstract_excerpt":"We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point index theory. Many examples and an application to boundary value problems are also included."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02487","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":"2026-05-18T00:59:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HumS/izzHvfz1yABEWRCKAYdfG9NMo7XMhs2VuvfPNuZeCMfnWrNbIu8P3kD0My73TyYvV02b77GHmqHX+xZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:49:03.098247Z"},"content_sha256":"ddc2491528de7d83c9a8890fe5c26e220f4f168948acc5162feccf8f852809c9","schema_version":"1.0","event_id":"sha256:ddc2491528de7d83c9a8890fe5c26e220f4f168948acc5162feccf8f852809c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE/bundle.json","state_url":"https://pith.science/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE/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":"2026-06-03T03:49:03Z","links":{"resolver":"https://pith.science/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE","bundle":"https://pith.science/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE/bundle.json","state":"https://pith.science/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJZA6BKDG3HM5FWDVWTDJVLTRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GJZA6BKDG3HM5FWDVWTDJVLTRE","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":"488d41b30dee56d4281dc85444b3c8d6d5f3befea3eb97448ba0ccb755b2d092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-08T11:51:06Z","title_canon_sha256":"8937d967870a4a2982c2b876e20bf4e1500f1fc56a703d5922b597714c8f2a08"},"schema_version":"1.0","source":{"id":"1611.02487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02487","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02487v1","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02487","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"pith_short_12","alias_value":"GJZA6BKDG3HM","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GJZA6BKDG3HM5FWD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GJZA6BKD","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:ddc2491528de7d83c9a8890fe5c26e220f4f168948acc5162feccf8f852809c9","target":"graph","created_at":"2026-05-18T00:59:51Z","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 obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point index theory. Many examples and an application to boundary value problems are also included.","authors_text":"F. Adri\\'an F. Tojo, Rub\\'en Figueroa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-08T11:51:06Z","title":"Fixed points of Hammerstein-type equations on general cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02487","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:e06d1b28c2a57fbb0dd7b712b0849839aff0c7d4bb14ec5c5e95b8d328de4812","target":"record","created_at":"2026-05-18T00:59:51Z","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":"488d41b30dee56d4281dc85444b3c8d6d5f3befea3eb97448ba0ccb755b2d092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-08T11:51:06Z","title_canon_sha256":"8937d967870a4a2982c2b876e20bf4e1500f1fc56a703d5922b597714c8f2a08"},"schema_version":"1.0","source":{"id":"1611.02487","kind":"arxiv","version":1}},"canonical_sha256":"32720f054336cece96c3ada634d57389343f4dabb9ffd66e52a7ce8373a8355c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32720f054336cece96c3ada634d57389343f4dabb9ffd66e52a7ce8373a8355c","first_computed_at":"2026-05-18T00:59:51.893282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:51.893282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rj4j/1/SkovkTsqklJpbR9m0VF6FgZMe/s/1G6ONEVvpa5HuGUGjrtcpB/Bus6TcGHXeOmrHfbW7lkzwRuGJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:51.894022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e06d1b28c2a57fbb0dd7b712b0849839aff0c7d4bb14ec5c5e95b8d328de4812","sha256:ddc2491528de7d83c9a8890fe5c26e220f4f168948acc5162feccf8f852809c9"],"state_sha256":"90413b34e38d48af55cc1fd248133c92d29f12adb76d88ebea8b54dbf7145807"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHfJTFla4l7i6WqPRbcWL4LxLpmWBt7STmzWYoUtBNUv4cTTgoh1wjWUIqFU0X6WU534kDUjx9EVyI2MD4AeBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:49:03.100143Z","bundle_sha256":"306daec4dd7dda7486641d1caec966743e28dff100663987371ccfd59317c8ce"}}