{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YL3UCLBRKWXXENVCVVCWV2YGVP","short_pith_number":"pith:YL3UCLBR","canonical_record":{"source":{"id":"0910.5408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T15:47:35Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"048e527834e2a82e8cfc059e35d5ecaaa1f190c549a7f43e872f0b417859c2c8","abstract_canon_sha256":"b635ebf19f5daeb5f4c71f224bac8ff82fcf316de9d4c1a08bcbb9e7362b16fb"},"schema_version":"1.0"},"canonical_sha256":"c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884","source":{"kind":"arxiv","id":"0910.5408","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5408","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5408v3","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5408","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"YL3UCLBRKWXX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YL3UCLBRKWXXENVC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YL3UCLBR","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YL3UCLBRKWXXENVCVVCWV2YGVP","target":"record","payload":{"canonical_record":{"source":{"id":"0910.5408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T15:47:35Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"048e527834e2a82e8cfc059e35d5ecaaa1f190c549a7f43e872f0b417859c2c8","abstract_canon_sha256":"b635ebf19f5daeb5f4c71f224bac8ff82fcf316de9d4c1a08bcbb9e7362b16fb"},"schema_version":"1.0"},"canonical_sha256":"c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:01.525146Z","signature_b64":"mPr/NdDHtGUr5aRTyjYjHUPfIMzDlAB9nbCDehGy9eDq+TXNkpQxsO7uQPFte1NFrGzDFLC1zHbrhZoMFXlVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884","last_reissued_at":"2026-05-18T04:26:01.524723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:01.524723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.5408","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvQJ8KpNJdqhgOTlQJm7+aISBhT52Sd8jTgICWocFNJbQQDpejVIMwpvTld7cLNfAsVQlOpx+o2IbzaJkwOmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:30:37.221864Z"},"content_sha256":"def535253d40212b47194959131039376e80c370f29dc99f3fcff625c86549b4","schema_version":"1.0","event_id":"sha256:def535253d40212b47194959131039376e80c370f29dc99f3fcff625c86549b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YL3UCLBRKWXXENVCVVCWV2YGVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymmetry of Outer Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Mladen Bestvina, Yael Algom-Kfir","submitted_at":"2009-10-28T15:47:35Z","abstract_excerpt":"We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm that induces d. There is an Out(F_n)-invariant potential \\Psi on Outer space such that when the Lipschitz norm is corrected by the derivative of \\Psi, the resulting norm is quasisymmetric. As an application, we give new proofs of two theorems of Handel-Mosher, that the Lipschitz metric is quasi-symmetric when restricted to a thick part of Outer space, and that there is a uniform bound, depending only on the rank, on the ratio of logs of growth rates of any irreducible outer automorphism f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5408","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T04:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xfHsm7IntRwZ+YJyg2jJqj42CGiveeIK11OtXlJgCerYxMSW6IM8eFB2FZvQHSYQpcE2oS+CzLg/A1iY8xgDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:30:37.222576Z"},"content_sha256":"b4ebba50f606f88f52ac07a27f5aab62babb9df3d1359224cd41d387f4cbd265","schema_version":"1.0","event_id":"sha256:b4ebba50f606f88f52ac07a27f5aab62babb9df3d1359224cd41d387f4cbd265"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YL3UCLBRKWXXENVCVVCWV2YGVP/bundle.json","state_url":"https://pith.science/pith/YL3UCLBRKWXXENVCVVCWV2YGVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YL3UCLBRKWXXENVCVVCWV2YGVP/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":"2026-05-27T02:30:37Z","links":{"resolver":"https://pith.science/pith/YL3UCLBRKWXXENVCVVCWV2YGVP","bundle":"https://pith.science/pith/YL3UCLBRKWXXENVCVVCWV2YGVP/bundle.json","state":"https://pith.science/pith/YL3UCLBRKWXXENVCVVCWV2YGVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YL3UCLBRKWXXENVCVVCWV2YGVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YL3UCLBRKWXXENVCVVCWV2YGVP","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":"b635ebf19f5daeb5f4c71f224bac8ff82fcf316de9d4c1a08bcbb9e7362b16fb","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T15:47:35Z","title_canon_sha256":"048e527834e2a82e8cfc059e35d5ecaaa1f190c549a7f43e872f0b417859c2c8"},"schema_version":"1.0","source":{"id":"0910.5408","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.5408","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"0910.5408v3","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5408","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"YL3UCLBRKWXX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YL3UCLBRKWXXENVC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YL3UCLBR","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:b4ebba50f606f88f52ac07a27f5aab62babb9df3d1359224cd41d387f4cbd265","target":"graph","created_at":"2026-05-18T04:26:01Z","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"},"paper":{"abstract_excerpt":"We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm that induces d. There is an Out(F_n)-invariant potential \\Psi on Outer space such that when the Lipschitz norm is corrected by the derivative of \\Psi, the resulting norm is quasisymmetric. As an application, we give new proofs of two theorems of Handel-Mosher, that the Lipschitz metric is quasi-symmetric when restricted to a thick part of Outer space, and that there is a uniform bound, depending only on the rank, on the ratio of logs of growth rates of any irreducible outer automorphism f","authors_text":"Mladen Bestvina, Yael Algom-Kfir","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T15:47:35Z","title":"Asymmetry of Outer Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5408","kind":"arxiv","version":3},"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:def535253d40212b47194959131039376e80c370f29dc99f3fcff625c86549b4","target":"record","created_at":"2026-05-18T04:26:01Z","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":"b635ebf19f5daeb5f4c71f224bac8ff82fcf316de9d4c1a08bcbb9e7362b16fb","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-10-28T15:47:35Z","title_canon_sha256":"048e527834e2a82e8cfc059e35d5ecaaa1f190c549a7f43e872f0b417859c2c8"},"schema_version":"1.0","source":{"id":"0910.5408","kind":"arxiv","version":3}},"canonical_sha256":"c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884","first_computed_at":"2026-05-18T04:26:01.524723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:01.524723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPr/NdDHtGUr5aRTyjYjHUPfIMzDlAB9nbCDehGy9eDq+TXNkpQxsO7uQPFte1NFrGzDFLC1zHbrhZoMFXlVAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:01.525146Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.5408","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:def535253d40212b47194959131039376e80c370f29dc99f3fcff625c86549b4","sha256:b4ebba50f606f88f52ac07a27f5aab62babb9df3d1359224cd41d387f4cbd265"],"state_sha256":"67267d5ef6a0433a707b2faa4d9f6dde816265a7252366177101f45a8e734135"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLsZ1ZqYMmoUuKrxECXcTewf+5XLh9LY4uVMeLEMAN3X4lSHR/4VWLkzp3HVOh6Ii8UXD2bgs7nXiZB+L3oMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:30:37.226640Z","bundle_sha256":"7232e5485d29b9e7f7b108c62c8b7e8c618e72ca008ab91e5b27aa5c00fd6d16"}}