{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LFAGD5AR7F4UDTB7GII7UM4DYD","short_pith_number":"pith:LFAGD5AR","canonical_record":{"source":{"id":"2308.14372","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-28T07:41:50Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b9fb52702826be904858db8b4c53fcd530dcc89a0cd6734f6274ff95d8cb98cc","abstract_canon_sha256":"593dfea626c765c0bc50c0aaec7436eca74a0ffda9ac2100f3cb15e12533f17c"},"schema_version":"1.0"},"canonical_sha256":"594061f411f97941cc3f3211fa3383c0d0eb20b56eda3cc4e8c817a4dfc3b9d5","source":{"kind":"arxiv","id":"2308.14372","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.14372","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2308.14372v2","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.14372","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"LFAGD5AR7F4U","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"LFAGD5AR7F4UDTB7","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"LFAGD5AR","created_at":"2026-07-05T09:57:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LFAGD5AR7F4UDTB7GII7UM4DYD","target":"record","payload":{"canonical_record":{"source":{"id":"2308.14372","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-28T07:41:50Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b9fb52702826be904858db8b4c53fcd530dcc89a0cd6734f6274ff95d8cb98cc","abstract_canon_sha256":"593dfea626c765c0bc50c0aaec7436eca74a0ffda9ac2100f3cb15e12533f17c"},"schema_version":"1.0"},"canonical_sha256":"594061f411f97941cc3f3211fa3383c0d0eb20b56eda3cc4e8c817a4dfc3b9d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:18.486160Z","signature_b64":"RKm8mPhOsbr5DD5UtCAc6uRAfJusN0RfVmBiRldCwQV+s61MhHD5VkXHv51xa6m+tcbn68jxiumy4iQeVnuFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"594061f411f97941cc3f3211fa3383c0d0eb20b56eda3cc4e8c817a4dfc3b9d5","last_reissued_at":"2026-07-05T09:57:18.485730Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:18.485730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.14372","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BhVg8CO6gEzPeZKCb8sIDJvd+l+SLstNC9X4H46N54x8YRO1qhPR7Jd/Wt2RonhZK0U2tWXrj/Smy8pdE+uEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:17:42.767980Z"},"content_sha256":"bf36df1db80fc1266cdfdde0330e88bfbec584bc4b41b7ea0da2e8cddb2be240","schema_version":"1.0","event_id":"sha256:bf36df1db80fc1266cdfdde0330e88bfbec584bc4b41b7ea0da2e8cddb2be240"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LFAGD5AR7F4UDTB7GII7UM4DYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polyhedral combinatorics of bisectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Aryaman Jal, Katharina Jochemko","submitted_at":"2023-08-28T07:41:50Z","abstract_excerpt":"For any polyhedral norm, the bisector of two points is a polyhedral complex. We study combinatorial aspects of this complex. We investigate the sensitivity of the presence of labelled maximal cells in the bisector relative to the position of the two points. We thereby extend work of Criado, Joswig and Santos (2022) who showed that for the tropical distance function the presence of maximal cells is encoded by a polyhedral fan, the bisection fan. We initiate the study of bisection cones and bisection fans with respect to arbitrary polyhedral norms. In particular, we show that the bisection fan a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.14372","kind":"arxiv","version":2},"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/2308.14372/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":"2026-07-05T09:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5uEdIUSYkCKIxxGqnyh3YNnvQZduVZRSU8zrdU++lEOb11apD0GcftnW6toia+0mc/UXOwt/8P7ZVLUjY7nJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:17:42.768311Z"},"content_sha256":"7a16a8a6a5a3a214defad6e38240daaea72c363dfcbe918879f2fee2c9aca07b","schema_version":"1.0","event_id":"sha256:7a16a8a6a5a3a214defad6e38240daaea72c363dfcbe918879f2fee2c9aca07b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFAGD5AR7F4UDTB7GII7UM4DYD/bundle.json","state_url":"https://pith.science/pith/LFAGD5AR7F4UDTB7GII7UM4DYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFAGD5AR7F4UDTB7GII7UM4DYD/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":"2026-08-13T17:17:42Z","links":{"resolver":"https://pith.science/pith/LFAGD5AR7F4UDTB7GII7UM4DYD","bundle":"https://pith.science/pith/LFAGD5AR7F4UDTB7GII7UM4DYD/bundle.json","state":"https://pith.science/pith/LFAGD5AR7F4UDTB7GII7UM4DYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFAGD5AR7F4UDTB7GII7UM4DYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LFAGD5AR7F4UDTB7GII7UM4DYD","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":"593dfea626c765c0bc50c0aaec7436eca74a0ffda9ac2100f3cb15e12533f17c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-28T07:41:50Z","title_canon_sha256":"b9fb52702826be904858db8b4c53fcd530dcc89a0cd6734f6274ff95d8cb98cc"},"schema_version":"1.0","source":{"id":"2308.14372","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.14372","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2308.14372v2","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.14372","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"LFAGD5AR7F4U","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"LFAGD5AR7F4UDTB7","created_at":"2026-07-05T09:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"LFAGD5AR","created_at":"2026-07-05T09:57:18Z"}],"graph_snapshots":[{"event_id":"sha256:7a16a8a6a5a3a214defad6e38240daaea72c363dfcbe918879f2fee2c9aca07b","target":"graph","created_at":"2026-07-05T09:57:18Z","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/2308.14372/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any polyhedral norm, the bisector of two points is a polyhedral complex. We study combinatorial aspects of this complex. We investigate the sensitivity of the presence of labelled maximal cells in the bisector relative to the position of the two points. We thereby extend work of Criado, Joswig and Santos (2022) who showed that for the tropical distance function the presence of maximal cells is encoded by a polyhedral fan, the bisection fan. We initiate the study of bisection cones and bisection fans with respect to arbitrary polyhedral norms. In particular, we show that the bisection fan a","authors_text":"Aryaman Jal, Katharina Jochemko","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-28T07:41:50Z","title":"Polyhedral combinatorics of bisectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.14372","kind":"arxiv","version":2},"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:bf36df1db80fc1266cdfdde0330e88bfbec584bc4b41b7ea0da2e8cddb2be240","target":"record","created_at":"2026-07-05T09:57:18Z","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":"593dfea626c765c0bc50c0aaec7436eca74a0ffda9ac2100f3cb15e12533f17c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-28T07:41:50Z","title_canon_sha256":"b9fb52702826be904858db8b4c53fcd530dcc89a0cd6734f6274ff95d8cb98cc"},"schema_version":"1.0","source":{"id":"2308.14372","kind":"arxiv","version":2}},"canonical_sha256":"594061f411f97941cc3f3211fa3383c0d0eb20b56eda3cc4e8c817a4dfc3b9d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"594061f411f97941cc3f3211fa3383c0d0eb20b56eda3cc4e8c817a4dfc3b9d5","first_computed_at":"2026-07-05T09:57:18.485730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:18.485730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RKm8mPhOsbr5DD5UtCAc6uRAfJusN0RfVmBiRldCwQV+s61MhHD5VkXHv51xa6m+tcbn68jxiumy4iQeVnuFAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:18.486160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.14372","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf36df1db80fc1266cdfdde0330e88bfbec584bc4b41b7ea0da2e8cddb2be240","sha256:7a16a8a6a5a3a214defad6e38240daaea72c363dfcbe918879f2fee2c9aca07b"],"state_sha256":"d9b7d864a47e6d370b886ae6acfdbf7f9b2ca35d9a8cf4a1a2bcc04bd7b2724f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Skjc2x4fwrD861tdutt5OxVRQTEINLh5bvHys4SiCAeLmg5rxhlFJyTQS8nax2aR/WhRCpmvBOVWv+M6aRmpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:17:42.789033Z","bundle_sha256":"608e00434b317a079bb557feb2f5260eca0ae788b667d65f62dcc6e84ba9e886"}}