{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4RQECB4XAZIIFFFRGWUBASZOYZ","short_pith_number":"pith:4RQECB4X","canonical_record":{"source":{"id":"2008.07310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-28T04:01:15Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"d48f49eb2d47df42b9aa312e4a4f9c45cc4aec605fec5b7402c6e047b4f21360","abstract_canon_sha256":"c479c8d54df34501997830585d9b8a6575a6bbf4f67a0eee9d44c9b495aea9dd"},"schema_version":"1.0"},"canonical_sha256":"e46041079706508294b135a8104b2ec67a3633c1f8ec687fc417b9df651b769a","source":{"kind":"arxiv","id":"2008.07310","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.07310","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"2008.07310v1","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07310","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"4RQECB4XAZII","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"4RQECB4XAZIIFFFR","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"4RQECB4X","created_at":"2026-07-05T01:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4RQECB4XAZIIFFFRGWUBASZOYZ","target":"record","payload":{"canonical_record":{"source":{"id":"2008.07310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-28T04:01:15Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"d48f49eb2d47df42b9aa312e4a4f9c45cc4aec605fec5b7402c6e047b4f21360","abstract_canon_sha256":"c479c8d54df34501997830585d9b8a6575a6bbf4f67a0eee9d44c9b495aea9dd"},"schema_version":"1.0"},"canonical_sha256":"e46041079706508294b135a8104b2ec67a3633c1f8ec687fc417b9df651b769a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:27:38.506801Z","signature_b64":"GIxCnH6VHXSdU7SfZ2aQPMTtW9pFUNe33ArUrqplDKBBpq4OYlkQhjvXBAR9G/x/gdoncQyIQR33hHuPytTwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e46041079706508294b135a8104b2ec67a3633c1f8ec687fc417b9df651b769a","last_reissued_at":"2026-07-05T01:27:38.506361Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:27:38.506361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.07310","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":"2026-07-05T01:27:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xn8LhCt/brV1NFrd7L1g08eMPAu3Oq4ucGihsCcXUPgqjwbRbb2KjUsd0Je9ic9X/IeYoXDh91XHk+xWuMXZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:11:50.157369Z"},"content_sha256":"6dfeea6447873b035e9ca2ee74ba2e47f0a16853e99992d0130da93945610bef","schema_version":"1.0","event_id":"sha256:6dfeea6447873b035e9ca2ee74ba2e47f0a16853e99992d0130da93945610bef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4RQECB4XAZIIFFFRGWUBASZOYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Daniele Mortari, David Anas","submitted_at":"2020-07-28T04:01:15Z","abstract_excerpt":"This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: a) complex mapping, b) projection mapping, and c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings having no closed-form inverse. The advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07310","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.07310/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:27:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnK/qACjuIB+otCTOF+76GC87PfNZ4I5FW4X9mN/y5dANdGhXJjvmy1Wv7dOkAmnT5+vhmO0ddq3L21/pId3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:11:50.157756Z"},"content_sha256":"ea2c3a6170fc16703a4de1408b41c19f17d0c8d94b0b4c3c669b952bfd8b2568","schema_version":"1.0","event_id":"sha256:ea2c3a6170fc16703a4de1408b41c19f17d0c8d94b0b4c3c669b952bfd8b2568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4RQECB4XAZIIFFFRGWUBASZOYZ/bundle.json","state_url":"https://pith.science/pith/4RQECB4XAZIIFFFRGWUBASZOYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4RQECB4XAZIIFFFRGWUBASZOYZ/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":"2026-07-09T04:11:50Z","links":{"resolver":"https://pith.science/pith/4RQECB4XAZIIFFFRGWUBASZOYZ","bundle":"https://pith.science/pith/4RQECB4XAZIIFFFRGWUBASZOYZ/bundle.json","state":"https://pith.science/pith/4RQECB4XAZIIFFFRGWUBASZOYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4RQECB4XAZIIFFFRGWUBASZOYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4RQECB4XAZIIFFFRGWUBASZOYZ","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":"c479c8d54df34501997830585d9b8a6575a6bbf4f67a0eee9d44c9b495aea9dd","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-28T04:01:15Z","title_canon_sha256":"d48f49eb2d47df42b9aa312e4a4f9c45cc4aec605fec5b7402c6e047b4f21360"},"schema_version":"1.0","source":{"id":"2008.07310","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.07310","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"2008.07310v1","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07310","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"4RQECB4XAZII","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"4RQECB4XAZIIFFFR","created_at":"2026-07-05T01:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"4RQECB4X","created_at":"2026-07-05T01:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:ea2c3a6170fc16703a4de1408b41c19f17d0c8d94b0b4c3c669b952bfd8b2568","target":"graph","created_at":"2026-07-05T01:27:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.07310/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: a) complex mapping, b) projection mapping, and c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings having no closed-form inverse. The advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace bound","authors_text":"Daniele Mortari, David Anas","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-28T04:01:15Z","title":"Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07310","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":"sha256:6dfeea6447873b035e9ca2ee74ba2e47f0a16853e99992d0130da93945610bef","target":"record","created_at":"2026-07-05T01:27:38Z","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":"c479c8d54df34501997830585d9b8a6575a6bbf4f67a0eee9d44c9b495aea9dd","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-28T04:01:15Z","title_canon_sha256":"d48f49eb2d47df42b9aa312e4a4f9c45cc4aec605fec5b7402c6e047b4f21360"},"schema_version":"1.0","source":{"id":"2008.07310","kind":"arxiv","version":1}},"canonical_sha256":"e46041079706508294b135a8104b2ec67a3633c1f8ec687fc417b9df651b769a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e46041079706508294b135a8104b2ec67a3633c1f8ec687fc417b9df651b769a","first_computed_at":"2026-07-05T01:27:38.506361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:27:38.506361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GIxCnH6VHXSdU7SfZ2aQPMTtW9pFUNe33ArUrqplDKBBpq4OYlkQhjvXBAR9G/x/gdoncQyIQR33hHuPytTwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:27:38.506801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.07310","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dfeea6447873b035e9ca2ee74ba2e47f0a16853e99992d0130da93945610bef","sha256:ea2c3a6170fc16703a4de1408b41c19f17d0c8d94b0b4c3c669b952bfd8b2568"],"state_sha256":"f193234e05279c0c048bc34fb3f43705b59f5548d30cb943aada8a2224b10d60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onsgz8oxRrkUqdTrfxIkpwonJKLMb9YMjLtSsB819Ismfv9VRwHir/6O7SWQ9LmMFY8bul9HZob2S+kHcFtbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T04:11:50.159864Z","bundle_sha256":"1aeefd1d7614aaa435d66b21cd5ff6429a876d938a8543436072e3a3f556fc10"}}