{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XHAYG5RZG65R6NXVXLRNRTHNSL","short_pith_number":"pith:XHAYG5RZ","canonical_record":{"source":{"id":"2505.07190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T02:40:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"dbe7dbd8396150e84883afd5b96dc71f05a1d925f4f423e56ca2db3fb6cb585b","abstract_canon_sha256":"691c2ae56ff0d8b345df579e917fbb28a955bc738c0bbc873024e9ecd78bc45e"},"schema_version":"1.0"},"canonical_sha256":"b9c183763937bb1f36f5bae2d8cced92ed8ae4d8ef83585913d176b6cf1f8cde","source":{"kind":"arxiv","id":"2505.07190","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.07190","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"2505.07190v1","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07190","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"XHAYG5RZG65R","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"pith_short_16","alias_value":"XHAYG5RZG65R6NXV","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"pith_short_8","alias_value":"XHAYG5RZ","created_at":"2026-07-05T11:01:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XHAYG5RZG65R6NXVXLRNRTHNSL","target":"record","payload":{"canonical_record":{"source":{"id":"2505.07190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T02:40:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"dbe7dbd8396150e84883afd5b96dc71f05a1d925f4f423e56ca2db3fb6cb585b","abstract_canon_sha256":"691c2ae56ff0d8b345df579e917fbb28a955bc738c0bbc873024e9ecd78bc45e"},"schema_version":"1.0"},"canonical_sha256":"b9c183763937bb1f36f5bae2d8cced92ed8ae4d8ef83585913d176b6cf1f8cde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:43.978203Z","signature_b64":"8QbeQBATa0E56nNJtlM8lT+mYRjMuFQZ8iI/iErZdRumWRi94IrINZf5sO/KHNhzNQbe26bvRLdyA5ETZdZ5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c183763937bb1f36f5bae2d8cced92ed8ae4d8ef83585913d176b6cf1f8cde","last_reissued_at":"2026-07-05T11:01:43.977805Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:43.977805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.07190","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":"2026-07-05T11:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CI9/JZl/lI6uDaeBk3v30syFelmfL7XFQxN1aRA0gTeMmpLlDQV/GTREe6/HLT640crIJtHcokc7cr/IY55lAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:52:47.610498Z"},"content_sha256":"96f2edcc5f67c67e2490afe2df08c89f8042efa9455a5d6397b9f6b1ab3fbd15","schema_version":"1.0","event_id":"sha256:96f2edcc5f67c67e2490afe2df08c89f8042efa9455a5d6397b9f6b1ab3fbd15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XHAYG5RZG65R6NXVXLRNRTHNSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connectedness of the boundaries of the strata of differentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Dawei Chen","submitted_at":"2025-05-12T02:40:16Z","abstract_excerpt":"Let $\\mathcal{P}(\\mu)^{\\circ}$ be a connected component of the projectivized stratum of differentials on smooth complex curves, where the zero and pole orders of the differentials are specified by $\\mu$. When the complex dimension of $\\mathcal{P}(\\mu)^{\\circ}$ is at least two, Dozier--Grushevsky--Lee, through explicit degeneration techniques, showed that the boundary of $\\mathcal{P}(\\mu)^{\\circ}$ is connected in the multi-scale compactification constructed by Bainbridge--Chen--Gendron--Grushevsky--M\\\"oller.\n  A natural question is whether the connectedness of the boundary of $\\mathcal{P}(\\mu)^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07190","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/2505.07190/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":"2026-07-05T11:01:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/5dVyZBAyD87T5rM9CRN6enLBYqMs+6+uQPCsf9kOcwvwgEeADUczbl7pLDHA+QE7Ziwkr4LN8odqHc0EEnVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:52:47.611052Z"},"content_sha256":"a86943b5eba420c242ee08acd1a4f16b63e520095406d3fcb899994854ce6e2b","schema_version":"1.0","event_id":"sha256:a86943b5eba420c242ee08acd1a4f16b63e520095406d3fcb899994854ce6e2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHAYG5RZG65R6NXVXLRNRTHNSL/bundle.json","state_url":"https://pith.science/pith/XHAYG5RZG65R6NXVXLRNRTHNSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHAYG5RZG65R6NXVXLRNRTHNSL/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":"2026-08-21T13:52:47Z","links":{"resolver":"https://pith.science/pith/XHAYG5RZG65R6NXVXLRNRTHNSL","bundle":"https://pith.science/pith/XHAYG5RZG65R6NXVXLRNRTHNSL/bundle.json","state":"https://pith.science/pith/XHAYG5RZG65R6NXVXLRNRTHNSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHAYG5RZG65R6NXVXLRNRTHNSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XHAYG5RZG65R6NXVXLRNRTHNSL","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":"691c2ae56ff0d8b345df579e917fbb28a955bc738c0bbc873024e9ecd78bc45e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T02:40:16Z","title_canon_sha256":"dbe7dbd8396150e84883afd5b96dc71f05a1d925f4f423e56ca2db3fb6cb585b"},"schema_version":"1.0","source":{"id":"2505.07190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.07190","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"2505.07190v1","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07190","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"XHAYG5RZG65R","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"pith_short_16","alias_value":"XHAYG5RZG65R6NXV","created_at":"2026-07-05T11:01:43Z"},{"alias_kind":"pith_short_8","alias_value":"XHAYG5RZ","created_at":"2026-07-05T11:01:43Z"}],"graph_snapshots":[{"event_id":"sha256:a86943b5eba420c242ee08acd1a4f16b63e520095406d3fcb899994854ce6e2b","target":"graph","created_at":"2026-07-05T11:01:43Z","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/2505.07190/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{P}(\\mu)^{\\circ}$ be a connected component of the projectivized stratum of differentials on smooth complex curves, where the zero and pole orders of the differentials are specified by $\\mu$. When the complex dimension of $\\mathcal{P}(\\mu)^{\\circ}$ is at least two, Dozier--Grushevsky--Lee, through explicit degeneration techniques, showed that the boundary of $\\mathcal{P}(\\mu)^{\\circ}$ is connected in the multi-scale compactification constructed by Bainbridge--Chen--Gendron--Grushevsky--M\\\"oller.\n  A natural question is whether the connectedness of the boundary of $\\mathcal{P}(\\mu)^","authors_text":"Dawei Chen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T02:40:16Z","title":"Connectedness of the boundaries of the strata of differentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07190","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":"sha256:96f2edcc5f67c67e2490afe2df08c89f8042efa9455a5d6397b9f6b1ab3fbd15","target":"record","created_at":"2026-07-05T11:01:43Z","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":"691c2ae56ff0d8b345df579e917fbb28a955bc738c0bbc873024e9ecd78bc45e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T02:40:16Z","title_canon_sha256":"dbe7dbd8396150e84883afd5b96dc71f05a1d925f4f423e56ca2db3fb6cb585b"},"schema_version":"1.0","source":{"id":"2505.07190","kind":"arxiv","version":1}},"canonical_sha256":"b9c183763937bb1f36f5bae2d8cced92ed8ae4d8ef83585913d176b6cf1f8cde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9c183763937bb1f36f5bae2d8cced92ed8ae4d8ef83585913d176b6cf1f8cde","first_computed_at":"2026-07-05T11:01:43.977805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:43.977805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8QbeQBATa0E56nNJtlM8lT+mYRjMuFQZ8iI/iErZdRumWRi94IrINZf5sO/KHNhzNQbe26bvRLdyA5ETZdZ5BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:43.978203Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.07190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96f2edcc5f67c67e2490afe2df08c89f8042efa9455a5d6397b9f6b1ab3fbd15","sha256:a86943b5eba420c242ee08acd1a4f16b63e520095406d3fcb899994854ce6e2b"],"state_sha256":"0e1c394a48f52a773a21e2aee3b6226c59393168414cf1fe6a00c3e85b0ab651"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TNxFWQZPJhW2i2l+i9Nh+HoDxF8pxLKMr+uI/DxYvNrZe0G4cSZzzKVZ7/aAbaPSXpROx6z6OgH1zHeqllpAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T13:52:47.615490Z","bundle_sha256":"b10f6c9c24e3b13609e6fc313a762b689eaf2c68636467f4d0c7f0ea30ea86e5"}}