{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:C46KH7XESOF4WFBL5BMMQH4UYQ","short_pith_number":"pith:C46KH7XE","canonical_record":{"source":{"id":"2312.13224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2023-12-20T17:47:19Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"360c86d32027a41b8231f676ee9c5e4d32a6866aeab4dffe0e203e3e53c2f6c7","abstract_canon_sha256":"da9ef9bb08f7fe00a896d459a17c67fbf8b61053060268d89d61373e1672af33"},"schema_version":"1.0"},"canonical_sha256":"173ca3fee4938bcb142be858c81f94c434209d29504d9d41e868ca548ab5b52a","source":{"kind":"arxiv","id":"2312.13224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13224","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13224v1","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13224","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"pith_short_12","alias_value":"C46KH7XESOF4","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"pith_short_16","alias_value":"C46KH7XESOF4WFBL","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"pith_short_8","alias_value":"C46KH7XE","created_at":"2026-07-05T07:26:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:C46KH7XESOF4WFBL5BMMQH4UYQ","target":"record","payload":{"canonical_record":{"source":{"id":"2312.13224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2023-12-20T17:47:19Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"360c86d32027a41b8231f676ee9c5e4d32a6866aeab4dffe0e203e3e53c2f6c7","abstract_canon_sha256":"da9ef9bb08f7fe00a896d459a17c67fbf8b61053060268d89d61373e1672af33"},"schema_version":"1.0"},"canonical_sha256":"173ca3fee4938bcb142be858c81f94c434209d29504d9d41e868ca548ab5b52a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:26:33.627919Z","signature_b64":"ALh3LWEr8fFL0yPh+lKFrFaT4TUuUumD8IddZgsclEpqePq7aGg9GJJU7lDcKwv9Xg07rbRxTUG4KIa/UrC7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"173ca3fee4938bcb142be858c81f94c434209d29504d9d41e868ca548ab5b52a","last_reissued_at":"2026-07-05T07:26:33.627425Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:26:33.627425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.13224","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":"2026-07-05T07:26:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"My78yzTMdlZ1KvyclWRbTMKSqFXzu0e1C1qOH3Xh47ykCSh9Q+HL/b0CizO5yvC8qD4vHgHgcFi6cuRLwMXKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:34:23.527353Z"},"content_sha256":"01b77f3de28f89be3e08fe900070cc31b7ab201113e692655c2812308703bc26","schema_version":"1.0","event_id":"sha256:01b77f3de28f89be3e08fe900070cc31b7ab201113e692655c2812308703bc26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:C46KH7XESOF4WFBL5BMMQH4UYQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Symplectic Packing Problems in Higher Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Kyler Siegel, Yuan Yao","submitted_at":"2023-12-20T17:47:19Z","abstract_excerpt":"Let $B^{2n}(R)$ denote the closed $2n$-dimensional symplectic ball of area $R$, and let $\\Sigma_g(L)$ be a closed symplectic surface of genus $g$ and area $L$. We prove that there is a symplectic embedding $\\bigsqcup_{i=1}^k B^4(R_i) \\times \\Sigma_g (L) \\overset{s}\\hookrightarrow \\operatorname{int}(B^4(R))\\times \\Sigma_g (L)$ if and only if there exists a symplectic embedding $\\bigsqcup_{i=1}^k B^4(R_i) \\overset{s}\\hookrightarrow \\mathrm{int}(B^4(R))$.\n  This lies in contrast with the standard higher dimensional ball packing problem $\\bigsqcup\\limits_{i=1}^k B^{2 n}(R_i)\\overset{s}\\hookrightar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13224","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/2312.13224/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":"2026-07-05T07:26:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UwEA7JR9LJa20YWrgAv0gAH17coVk9OeRD0ekeHeszfdM1e2IfZ+KKVxvf6yVHwkD9Tsffo5wnODv5etNnVuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:34:23.528176Z"},"content_sha256":"cceb7d80b63e4d58d63cdc4b940c17f4e81d8e41b68a5082ef6d3a682d4fd1e1","schema_version":"1.0","event_id":"sha256:cceb7d80b63e4d58d63cdc4b940c17f4e81d8e41b68a5082ef6d3a682d4fd1e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C46KH7XESOF4WFBL5BMMQH4UYQ/bundle.json","state_url":"https://pith.science/pith/C46KH7XESOF4WFBL5BMMQH4UYQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C46KH7XESOF4WFBL5BMMQH4UYQ/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":"2026-08-19T22:34:23Z","links":{"resolver":"https://pith.science/pith/C46KH7XESOF4WFBL5BMMQH4UYQ","bundle":"https://pith.science/pith/C46KH7XESOF4WFBL5BMMQH4UYQ/bundle.json","state":"https://pith.science/pith/C46KH7XESOF4WFBL5BMMQH4UYQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C46KH7XESOF4WFBL5BMMQH4UYQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:C46KH7XESOF4WFBL5BMMQH4UYQ","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":"da9ef9bb08f7fe00a896d459a17c67fbf8b61053060268d89d61373e1672af33","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2023-12-20T17:47:19Z","title_canon_sha256":"360c86d32027a41b8231f676ee9c5e4d32a6866aeab4dffe0e203e3e53c2f6c7"},"schema_version":"1.0","source":{"id":"2312.13224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13224","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13224v1","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13224","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"pith_short_12","alias_value":"C46KH7XESOF4","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"pith_short_16","alias_value":"C46KH7XESOF4WFBL","created_at":"2026-07-05T07:26:33Z"},{"alias_kind":"pith_short_8","alias_value":"C46KH7XE","created_at":"2026-07-05T07:26:33Z"}],"graph_snapshots":[{"event_id":"sha256:cceb7d80b63e4d58d63cdc4b940c17f4e81d8e41b68a5082ef6d3a682d4fd1e1","target":"graph","created_at":"2026-07-05T07:26:33Z","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/2312.13224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $B^{2n}(R)$ denote the closed $2n$-dimensional symplectic ball of area $R$, and let $\\Sigma_g(L)$ be a closed symplectic surface of genus $g$ and area $L$. We prove that there is a symplectic embedding $\\bigsqcup_{i=1}^k B^4(R_i) \\times \\Sigma_g (L) \\overset{s}\\hookrightarrow \\operatorname{int}(B^4(R))\\times \\Sigma_g (L)$ if and only if there exists a symplectic embedding $\\bigsqcup_{i=1}^k B^4(R_i) \\overset{s}\\hookrightarrow \\mathrm{int}(B^4(R))$.\n  This lies in contrast with the standard higher dimensional ball packing problem $\\bigsqcup\\limits_{i=1}^k B^{2 n}(R_i)\\overset{s}\\hookrightar","authors_text":"Kyler Siegel, Yuan Yao","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2023-12-20T17:47:19Z","title":"On Symplectic Packing Problems in Higher Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13224","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":"sha256:01b77f3de28f89be3e08fe900070cc31b7ab201113e692655c2812308703bc26","target":"record","created_at":"2026-07-05T07:26:33Z","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":"da9ef9bb08f7fe00a896d459a17c67fbf8b61053060268d89d61373e1672af33","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2023-12-20T17:47:19Z","title_canon_sha256":"360c86d32027a41b8231f676ee9c5e4d32a6866aeab4dffe0e203e3e53c2f6c7"},"schema_version":"1.0","source":{"id":"2312.13224","kind":"arxiv","version":1}},"canonical_sha256":"173ca3fee4938bcb142be858c81f94c434209d29504d9d41e868ca548ab5b52a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"173ca3fee4938bcb142be858c81f94c434209d29504d9d41e868ca548ab5b52a","first_computed_at":"2026-07-05T07:26:33.627425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:26:33.627425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ALh3LWEr8fFL0yPh+lKFrFaT4TUuUumD8IddZgsclEpqePq7aGg9GJJU7lDcKwv9Xg07rbRxTUG4KIa/UrC7Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:26:33.627919Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.13224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01b77f3de28f89be3e08fe900070cc31b7ab201113e692655c2812308703bc26","sha256:cceb7d80b63e4d58d63cdc4b940c17f4e81d8e41b68a5082ef6d3a682d4fd1e1"],"state_sha256":"4010c4466bb60ad9afe13d0a4d6f8b728e4ecefd7691c6cd0e88b336aeda149d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YtaEhhIrmBE3vdlv696iHPGlIRIxUsJR6Gk/wd8wnLkSiG91ipdUSXVIbP9PDcK2P3y340DI+cmPueaWsBXcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:34:23.533227Z","bundle_sha256":"f019628aa544c527f1d9fa41d471b0feaa43bc2b52f5d4515a211cfc5b573435"}}