{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SHRHJFBPL3W5DV7FOFJ7I2QJEN","short_pith_number":"pith:SHRHJFBP","canonical_record":{"source":{"id":"1910.07923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-17T14:01:27Z","cross_cats_sorted":[],"title_canon_sha256":"571e90b56214efefe2f9ba2f78e3b94d48c59ab7ed6b2ac64592b9dde20cc194","abstract_canon_sha256":"6c50fe1a0189c049ca01bcca588ef1d002477c140db8e843e359ac7e7f6a3ae7"},"schema_version":"1.0"},"canonical_sha256":"91e274942f5eedd1d7e57153f46a09235f646d0807574fa7447aebff92171d24","source":{"kind":"arxiv","id":"1910.07923","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07923","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07923v1","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07923","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"SHRHJFBPL3W5","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"pith_short_16","alias_value":"SHRHJFBPL3W5DV7F","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"pith_short_8","alias_value":"SHRHJFBP","created_at":"2026-07-05T00:12:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SHRHJFBPL3W5DV7FOFJ7I2QJEN","target":"record","payload":{"canonical_record":{"source":{"id":"1910.07923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-17T14:01:27Z","cross_cats_sorted":[],"title_canon_sha256":"571e90b56214efefe2f9ba2f78e3b94d48c59ab7ed6b2ac64592b9dde20cc194","abstract_canon_sha256":"6c50fe1a0189c049ca01bcca588ef1d002477c140db8e843e359ac7e7f6a3ae7"},"schema_version":"1.0"},"canonical_sha256":"91e274942f5eedd1d7e57153f46a09235f646d0807574fa7447aebff92171d24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:12:57.121555Z","signature_b64":"YaLQEBXYUU2simBp8HHYTj2Qa/AG+v25Z8sMqZDf4Fsr43l/1R4BD7us2nqc1nCjXAye4yD6nVZuq84IsmDMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91e274942f5eedd1d7e57153f46a09235f646d0807574fa7447aebff92171d24","last_reissued_at":"2026-07-05T00:12:57.121104Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:12:57.121104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.07923","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":"2026-07-05T00:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zg9gJqhhbV5eQGptQ9ZDogpv7Zjn9ScN95M3YJqjmvsRrHtuu55KDDXw7sRc21kdM5C/dvYAOHAlTdXZTrGhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-23T11:05:32.322647Z"},"content_sha256":"07c8ceada005fa4017bc2575ab86748bb60f416287d51d591b486c2276f84072","schema_version":"1.0","event_id":"sha256:07c8ceada005fa4017bc2575ab86748bb60f416287d51d591b486c2276f84072"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SHRHJFBPL3W5DV7FOFJ7I2QJEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some results on isometric composition operators on Lipschitz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca","submitted_at":"2019-10-17T14:01:27Z","abstract_excerpt":"Given two metric spaces $M$ and $N$ we study, motivated by a question of N. Weaver, conditions under which an isometric composition operator $C_\\phi:\\mathrm{Lip}_0(M)\\longrightarrow \\mathrm{Lip}_0(N)$ is isometric depending on the properties of $\\phi$. We obtain a complete characterisation of those operators $C_\\phi$ in terms of a property of the function $\\phi$ in the case that $B_{\\mathcal F(M)}$ is the closed convex hull of its preserved extreme points. Also, we obtain necessary and sufficient conditions for $C_\\phi$ being isometric in the case that $M$ is geodesic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07923","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/1910.07923/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":"2026-07-05T00:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EmSol2ZvnmvgjEA4y6740frSMGjvZJSRNmGc1f0OKf6JqwvFeUe9nqHbMp48oMzkUC3UZtapw8PZX85Gg+C1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-23T11:05:32.323022Z"},"content_sha256":"233e648f4859745cee42b75ad9e413840c76c21cba9bd0c05c55453ea6fe406f","schema_version":"1.0","event_id":"sha256:233e648f4859745cee42b75ad9e413840c76c21cba9bd0c05c55453ea6fe406f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN/bundle.json","state_url":"https://pith.science/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN/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":"2026-07-23T11:05:32Z","links":{"resolver":"https://pith.science/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN","bundle":"https://pith.science/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN/bundle.json","state":"https://pith.science/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHRHJFBPL3W5DV7FOFJ7I2QJEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SHRHJFBPL3W5DV7FOFJ7I2QJEN","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":"6c50fe1a0189c049ca01bcca588ef1d002477c140db8e843e359ac7e7f6a3ae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-17T14:01:27Z","title_canon_sha256":"571e90b56214efefe2f9ba2f78e3b94d48c59ab7ed6b2ac64592b9dde20cc194"},"schema_version":"1.0","source":{"id":"1910.07923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07923","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07923v1","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07923","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"SHRHJFBPL3W5","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"pith_short_16","alias_value":"SHRHJFBPL3W5DV7F","created_at":"2026-07-05T00:12:57Z"},{"alias_kind":"pith_short_8","alias_value":"SHRHJFBP","created_at":"2026-07-05T00:12:57Z"}],"graph_snapshots":[{"event_id":"sha256:233e648f4859745cee42b75ad9e413840c76c21cba9bd0c05c55453ea6fe406f","target":"graph","created_at":"2026-07-05T00:12:57Z","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/1910.07923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given two metric spaces $M$ and $N$ we study, motivated by a question of N. Weaver, conditions under which an isometric composition operator $C_\\phi:\\mathrm{Lip}_0(M)\\longrightarrow \\mathrm{Lip}_0(N)$ is isometric depending on the properties of $\\phi$. We obtain a complete characterisation of those operators $C_\\phi$ in terms of a property of the function $\\phi$ in the case that $B_{\\mathcal F(M)}$ is the closed convex hull of its preserved extreme points. Also, we obtain necessary and sufficient conditions for $C_\\phi$ being isometric in the case that $M$ is geodesic.","authors_text":"Abraham Rueda Zoca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-17T14:01:27Z","title":"Some results on isometric composition operators on Lipschitz spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07923","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":"sha256:07c8ceada005fa4017bc2575ab86748bb60f416287d51d591b486c2276f84072","target":"record","created_at":"2026-07-05T00:12:57Z","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":"6c50fe1a0189c049ca01bcca588ef1d002477c140db8e843e359ac7e7f6a3ae7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-17T14:01:27Z","title_canon_sha256":"571e90b56214efefe2f9ba2f78e3b94d48c59ab7ed6b2ac64592b9dde20cc194"},"schema_version":"1.0","source":{"id":"1910.07923","kind":"arxiv","version":1}},"canonical_sha256":"91e274942f5eedd1d7e57153f46a09235f646d0807574fa7447aebff92171d24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91e274942f5eedd1d7e57153f46a09235f646d0807574fa7447aebff92171d24","first_computed_at":"2026-07-05T00:12:57.121104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:12:57.121104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YaLQEBXYUU2simBp8HHYTj2Qa/AG+v25Z8sMqZDf4Fsr43l/1R4BD7us2nqc1nCjXAye4yD6nVZuq84IsmDMDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:12:57.121555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.07923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07c8ceada005fa4017bc2575ab86748bb60f416287d51d591b486c2276f84072","sha256:233e648f4859745cee42b75ad9e413840c76c21cba9bd0c05c55453ea6fe406f"],"state_sha256":"8e2acfe38c7ba7f17d31770aaa50b2f76bd30faf29dec4c9597cf083e41f7e45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i8y5f1dQ8r9IY9czFiBJDJ6F/VvfWECxhpnofpC49tKQyCo0amgjgPdvXLG9rAeuSVeuvGANuV6YnYa/DX2MCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-23T11:05:32.325424Z","bundle_sha256":"b0c639e4181dd424b94dbd47e2c7f9cb79a325c9f1999d64302d6db29b8136c7"}}