{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:CK6Z5VR5CXIEHWUMMM5VFOGI42","short_pith_number":"pith:CK6Z5VR5","canonical_record":{"source":{"id":"2006.16930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2020-06-29T11:58:03Z","cross_cats_sorted":[],"title_canon_sha256":"3a3f0043acb9dcb419c3891315a7c2eb9d20267eef715e5a9a8673a8841dc174","abstract_canon_sha256":"8bef535c437a0ff8d846ac5027ab156038f1a9ba7b4e7aac22dddef898abd4de"},"schema_version":"1.0"},"canonical_sha256":"12bd9ed63d15d043da8c633b52b8c8e69152dff8449ed881a5977674a5060331","source":{"kind":"arxiv","id":"2006.16930","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16930","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16930v1","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16930","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"CK6Z5VR5CXIE","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"pith_short_16","alias_value":"CK6Z5VR5CXIEHWUM","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"pith_short_8","alias_value":"CK6Z5VR5","created_at":"2026-07-05T03:35:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:CK6Z5VR5CXIEHWUMMM5VFOGI42","target":"record","payload":{"canonical_record":{"source":{"id":"2006.16930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2020-06-29T11:58:03Z","cross_cats_sorted":[],"title_canon_sha256":"3a3f0043acb9dcb419c3891315a7c2eb9d20267eef715e5a9a8673a8841dc174","abstract_canon_sha256":"8bef535c437a0ff8d846ac5027ab156038f1a9ba7b4e7aac22dddef898abd4de"},"schema_version":"1.0"},"canonical_sha256":"12bd9ed63d15d043da8c633b52b8c8e69152dff8449ed881a5977674a5060331","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:35:06.307808Z","signature_b64":"kEReoiJKU5TdMfCd3747WYNHtlRB7PEyx3GGlIyu0+R4Q1zYIsYVOHjIU5WGQnARZh2zaRhyXZtymKkM0wbnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12bd9ed63d15d043da8c633b52b8c8e69152dff8449ed881a5977674a5060331","last_reissued_at":"2026-07-05T03:35:06.307298Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:35:06.307298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.16930","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":"2026-07-05T03:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IYLr98Ei6Jnh+EBo6fvsr6VV45j92pJs4i0052JmBJHb6VnMYNS8MyIYqKEc5XeVInQHw9SHpaHDV+qKQysDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:38:51.250775Z"},"content_sha256":"f4ea15af592bcbc0d77d4e766e45eb176cc879942f53652e163a3fe2ccb07ca8","schema_version":"1.0","event_id":"sha256:f4ea15af592bcbc0d77d4e766e45eb176cc879942f53652e163a3fe2ccb07ca8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:CK6Z5VR5CXIEHWUMMM5VFOGI42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new Hodge operator in Discrete Exterior Calculus. Application to fluid mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CE","authors_text":"Aziz Hamdouni, Dina Razafindralandy, Rama Ayoub","submitted_at":"2020-06-29T11:58:03Z","abstract_excerpt":"This article introduces a new and general construction of discrete Hodge operator in the context of Discrete Exterior Calculus (DEC). This discrete Hodge operator enables to circumvent the well-centeredness limitation on the mesh with the popular diagonal Hodge. It allows a dual mesh based on any interior point, such as the incenter or the barycenter. It opens the way towards mesh-optimized discrete Hodge operators. In the particular case of a well-centered triangulation, it reduces to the diagonal Hodge if the dual mesh is circumcentric. Based on an analytical development, this discrete Hodge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16930","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/2006.16930/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":"2026-07-05T03:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VTfrUVeYSC8orIQgYaNa1H3MpdWGurqz0SrsWS+6wZIEB8RD4sfKItzGx9ITD8EYF9uvAwT9JsdnpU8s6+bCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:38:51.251174Z"},"content_sha256":"e3ae7826d212e97741d84262aa10ec2d429dcaeb2f3dbc10c26f2ca61c3262b0","schema_version":"1.0","event_id":"sha256:e3ae7826d212e97741d84262aa10ec2d429dcaeb2f3dbc10c26f2ca61c3262b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42/bundle.json","state_url":"https://pith.science/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42/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":"2026-07-07T08:38:51Z","links":{"resolver":"https://pith.science/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42","bundle":"https://pith.science/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42/bundle.json","state":"https://pith.science/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CK6Z5VR5CXIEHWUMMM5VFOGI42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CK6Z5VR5CXIEHWUMMM5VFOGI42","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":"8bef535c437a0ff8d846ac5027ab156038f1a9ba7b4e7aac22dddef898abd4de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2020-06-29T11:58:03Z","title_canon_sha256":"3a3f0043acb9dcb419c3891315a7c2eb9d20267eef715e5a9a8673a8841dc174"},"schema_version":"1.0","source":{"id":"2006.16930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16930","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16930v1","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16930","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"CK6Z5VR5CXIE","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"pith_short_16","alias_value":"CK6Z5VR5CXIEHWUM","created_at":"2026-07-05T03:35:06Z"},{"alias_kind":"pith_short_8","alias_value":"CK6Z5VR5","created_at":"2026-07-05T03:35:06Z"}],"graph_snapshots":[{"event_id":"sha256:e3ae7826d212e97741d84262aa10ec2d429dcaeb2f3dbc10c26f2ca61c3262b0","target":"graph","created_at":"2026-07-05T03:35:06Z","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/2006.16930/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article introduces a new and general construction of discrete Hodge operator in the context of Discrete Exterior Calculus (DEC). This discrete Hodge operator enables to circumvent the well-centeredness limitation on the mesh with the popular diagonal Hodge. It allows a dual mesh based on any interior point, such as the incenter or the barycenter. It opens the way towards mesh-optimized discrete Hodge operators. In the particular case of a well-centered triangulation, it reduces to the diagonal Hodge if the dual mesh is circumcentric. Based on an analytical development, this discrete Hodge","authors_text":"Aziz Hamdouni, Dina Razafindralandy, Rama Ayoub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2020-06-29T11:58:03Z","title":"A new Hodge operator in Discrete Exterior Calculus. Application to fluid mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16930","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:f4ea15af592bcbc0d77d4e766e45eb176cc879942f53652e163a3fe2ccb07ca8","target":"record","created_at":"2026-07-05T03:35:06Z","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":"8bef535c437a0ff8d846ac5027ab156038f1a9ba7b4e7aac22dddef898abd4de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2020-06-29T11:58:03Z","title_canon_sha256":"3a3f0043acb9dcb419c3891315a7c2eb9d20267eef715e5a9a8673a8841dc174"},"schema_version":"1.0","source":{"id":"2006.16930","kind":"arxiv","version":1}},"canonical_sha256":"12bd9ed63d15d043da8c633b52b8c8e69152dff8449ed881a5977674a5060331","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12bd9ed63d15d043da8c633b52b8c8e69152dff8449ed881a5977674a5060331","first_computed_at":"2026-07-05T03:35:06.307298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:35:06.307298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kEReoiJKU5TdMfCd3747WYNHtlRB7PEyx3GGlIyu0+R4Q1zYIsYVOHjIU5WGQnARZh2zaRhyXZtymKkM0wbnDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:35:06.307808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.16930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4ea15af592bcbc0d77d4e766e45eb176cc879942f53652e163a3fe2ccb07ca8","sha256:e3ae7826d212e97741d84262aa10ec2d429dcaeb2f3dbc10c26f2ca61c3262b0"],"state_sha256":"c801460bb9c1416ec7c76c190ef4e097998856f1e1bc232639996490ef57fe03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkcIuzrG2jqglSWVoheuYZPGoc49AhzUa7hnjug2Q8QeZSAPynvG4IRFyLOXlJ8aOUQ3w4R+0XlQhQrwNfOgBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:38:51.253126Z","bundle_sha256":"a9bc7aa51e0b4daff3e1ad2ef69a608851597c154e24c78713defc818876273b"}}