{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SBYDDJKCN5EFM2LS2L3YIJTWHD","short_pith_number":"pith:SBYDDJKC","canonical_record":{"source":{"id":"2506.23498","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-06-30T03:44:10Z","cross_cats_sorted":[],"title_canon_sha256":"75e3f6442cb1445d6fef3145f291a985ce4d21d8fac17f34464e41490e5f98fb","abstract_canon_sha256":"1aa8ed2c7010bf1706528877800e8d94c1fe7ccb8e21bd9d6dfba22772805e86"},"schema_version":"1.0"},"canonical_sha256":"907031a5426f48566972d2f784267638f430fac04f607919e269b85e6586d5af","source":{"kind":"arxiv","id":"2506.23498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23498","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23498v2","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23498","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"SBYDDJKCN5EF","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_16","alias_value":"SBYDDJKCN5EFM2LS","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_8","alias_value":"SBYDDJKC","created_at":"2026-07-03T00:16:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SBYDDJKCN5EFM2LS2L3YIJTWHD","target":"record","payload":{"canonical_record":{"source":{"id":"2506.23498","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-06-30T03:44:10Z","cross_cats_sorted":[],"title_canon_sha256":"75e3f6442cb1445d6fef3145f291a985ce4d21d8fac17f34464e41490e5f98fb","abstract_canon_sha256":"1aa8ed2c7010bf1706528877800e8d94c1fe7ccb8e21bd9d6dfba22772805e86"},"schema_version":"1.0"},"canonical_sha256":"907031a5426f48566972d2f784267638f430fac04f607919e269b85e6586d5af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T00:16:49.998634Z","signature_b64":"q4sO03nQ+Cij8rlXiMgG+RgPkDpXQu/Ux0pGLkrnzcFZcx4vZQe4MhRLraAZRJ04PZlwUomJyfHIfBB1w04vBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"907031a5426f48566972d2f784267638f430fac04f607919e269b85e6586d5af","last_reissued_at":"2026-07-03T00:16:49.998139Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T00:16:49.998139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.23498","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":"2026-07-03T00:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"51qU8mutUEIOoTtb1lA8x8O0IxGk2mbttKJta/awq0c6RnaLX9XRGT1RVceDJa1UJ+74LvRoAT8bTFQtXsroBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:41:24.765523Z"},"content_sha256":"65c697907c417bea9afb117d2859ee89fdd9050ff394fd1baeb16bad5f3f477c","schema_version":"1.0","event_id":"sha256:65c697907c417bea9afb117d2859ee89fdd9050ff394fd1baeb16bad5f3f477c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SBYDDJKCN5EFM2LS2L3YIJTWHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvy points, the perimeter, and the complexity of convex toric domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dan Cristofaro-Gardiner, Dusa McDuff, Nicki Magill","submitted_at":"2025-06-30T03:44:10Z","abstract_excerpt":"We study the related notions of curvature and perimeter for toric boundaries and their implications for symplectic packing problems in dimension 4; a natural setting for this is a generalized version of convex toric domain which we also study, where there are no conditions on the moment polytope at all aside from convexity.\n  We show that the subleading asymptotics of the ECH and elementary ECH capacities recover the perimeter of such domains in their liminf, without any genericity required, and hence the perimeter is an obstruction to a full filling. As an application, we give the first examp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23498","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/2506.23498/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":"2026-07-03T00:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0+XuohsF+07mFr6iKUIRE+h0Tdmkrr73gOt3UW3W3gpw8rC+P13KHlmfQUOBbUBFIdxQo/NWcAeSq5W7uM5RDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:41:24.766083Z"},"content_sha256":"81c2e8427441d09bbd1c05ae684e17b606f12d0ea648328da580aece899c3a37","schema_version":"1.0","event_id":"sha256:81c2e8427441d09bbd1c05ae684e17b606f12d0ea648328da580aece899c3a37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD/bundle.json","state_url":"https://pith.science/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD/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":"2026-08-09T00:41:24Z","links":{"resolver":"https://pith.science/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD","bundle":"https://pith.science/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD/bundle.json","state":"https://pith.science/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBYDDJKCN5EFM2LS2L3YIJTWHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SBYDDJKCN5EFM2LS2L3YIJTWHD","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":"1aa8ed2c7010bf1706528877800e8d94c1fe7ccb8e21bd9d6dfba22772805e86","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-06-30T03:44:10Z","title_canon_sha256":"75e3f6442cb1445d6fef3145f291a985ce4d21d8fac17f34464e41490e5f98fb"},"schema_version":"1.0","source":{"id":"2506.23498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23498","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23498v2","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23498","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"SBYDDJKCN5EF","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_16","alias_value":"SBYDDJKCN5EFM2LS","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_8","alias_value":"SBYDDJKC","created_at":"2026-07-03T00:16:49Z"}],"graph_snapshots":[{"event_id":"sha256:81c2e8427441d09bbd1c05ae684e17b606f12d0ea648328da580aece899c3a37","target":"graph","created_at":"2026-07-03T00:16:49Z","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/2506.23498/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the related notions of curvature and perimeter for toric boundaries and their implications for symplectic packing problems in dimension 4; a natural setting for this is a generalized version of convex toric domain which we also study, where there are no conditions on the moment polytope at all aside from convexity.\n  We show that the subleading asymptotics of the ECH and elementary ECH capacities recover the perimeter of such domains in their liminf, without any genericity required, and hence the perimeter is an obstruction to a full filling. As an application, we give the first examp","authors_text":"Dan Cristofaro-Gardiner, Dusa McDuff, Nicki Magill","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-06-30T03:44:10Z","title":"Curvy points, the perimeter, and the complexity of convex toric domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23498","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":"sha256:65c697907c417bea9afb117d2859ee89fdd9050ff394fd1baeb16bad5f3f477c","target":"record","created_at":"2026-07-03T00:16:49Z","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":"1aa8ed2c7010bf1706528877800e8d94c1fe7ccb8e21bd9d6dfba22772805e86","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-06-30T03:44:10Z","title_canon_sha256":"75e3f6442cb1445d6fef3145f291a985ce4d21d8fac17f34464e41490e5f98fb"},"schema_version":"1.0","source":{"id":"2506.23498","kind":"arxiv","version":2}},"canonical_sha256":"907031a5426f48566972d2f784267638f430fac04f607919e269b85e6586d5af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"907031a5426f48566972d2f784267638f430fac04f607919e269b85e6586d5af","first_computed_at":"2026-07-03T00:16:49.998139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T00:16:49.998139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4sO03nQ+Cij8rlXiMgG+RgPkDpXQu/Ux0pGLkrnzcFZcx4vZQe4MhRLraAZRJ04PZlwUomJyfHIfBB1w04vBw==","signature_status":"signed_v1","signed_at":"2026-07-03T00:16:49.998634Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.23498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65c697907c417bea9afb117d2859ee89fdd9050ff394fd1baeb16bad5f3f477c","sha256:81c2e8427441d09bbd1c05ae684e17b606f12d0ea648328da580aece899c3a37"],"state_sha256":"c299ce986716655c081dff838d3bd605db9a1eedeb3318513755223547447341"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNOPW3LOGOoAGStmKJ14OT2cOG86khhBYRJRuFgwib72K43X0OWpsPjVVucEZ/X3Oxi1xDat3MVBtUi6cfJsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:41:24.770375Z","bundle_sha256":"b1003ba0bb02c6e884131745084d33d5b57da9498a90ebea7eff5e0cbde6e9ff"}}