{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:IZ3Y2DWMI2C6OEEKOORVHE7CZB","short_pith_number":"pith:IZ3Y2DWM","canonical_record":{"source":{"id":"0803.0640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-03-05T12:02:38Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"8b7e178b6722da176c5f2e0d50d4410c716e5c04eb7243d3cc5eec04b6d45f55","abstract_canon_sha256":"d90a930f3b087b73deb2c41b3527d65628c0313de9734008f4ec9240fe7bd4f3"},"schema_version":"1.0"},"canonical_sha256":"46778d0ecc4685e7108a73a35393e2c879705fe61425a65a5925a41b57d7fe22","source":{"kind":"arxiv","id":"0803.0640","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.0640","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"0803.0640v2","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.0640","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"IZ3Y2DWMI2C6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IZ3Y2DWMI2C6OEEK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IZ3Y2DWM","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:IZ3Y2DWMI2C6OEEKOORVHE7CZB","target":"record","payload":{"canonical_record":{"source":{"id":"0803.0640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-03-05T12:02:38Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"8b7e178b6722da176c5f2e0d50d4410c716e5c04eb7243d3cc5eec04b6d45f55","abstract_canon_sha256":"d90a930f3b087b73deb2c41b3527d65628c0313de9734008f4ec9240fe7bd4f3"},"schema_version":"1.0"},"canonical_sha256":"46778d0ecc4685e7108a73a35393e2c879705fe61425a65a5925a41b57d7fe22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:13.884003Z","signature_b64":"B+DndSrQWRdTmCX4t3r5OYeIy3bdGBVLmTT+ZsYDCNS0cursnpXJq653T5kjI3DuKeIjZeP+ub1DlyJgd1zeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46778d0ecc4685e7108a73a35393e2c879705fe61425a65a5925a41b57d7fe22","last_reissued_at":"2026-05-18T04:17:13.883567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:13.883567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.0640","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":"2026-05-18T04:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6nFDikCN6dhjXmyDZ9kNx4fRxdBUOGQQl2qch/XXM5twoVe6HmW4dhSoy+sPGxNK5Zfk4I1ldqDiAmbO/+YAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:21:32.080066Z"},"content_sha256":"068d166f44f1ffe69fa7e812f4e5f1b4b5270527bf2274b539c7a6c480a7d306","schema_version":"1.0","event_id":"sha256:068d166f44f1ffe69fa7e812f4e5f1b4b5270527bf2274b539c7a6c480a7d306"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:IZ3Y2DWMI2C6OEEKOORVHE7CZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric properties of Outer Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Armando Martino, Stefano Francaviglia","submitted_at":"2008-03-05T12:02:38Z","abstract_excerpt":"We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metric graphs in an easy way and we discuss the behaviour of stretching factors under iterations of automorphisms. We study metric properties of folding paths, showing that they are geodesic for the non-symm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.0640","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":""},"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":"2026-05-18T04:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FvUXE3/tKQ1V3hhCBo2FE1CGk44Q5FI9L5OGpZV8/kvfvrYoBvp+n2zcUb4Ijzk9YT9cJMgYkmkJ4TteGb56Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:21:32.080409Z"},"content_sha256":"f3b3e8f1ff4425c858d5478932b2b376ad84f2838fe1daf1626f917090bee3d7","schema_version":"1.0","event_id":"sha256:f3b3e8f1ff4425c858d5478932b2b376ad84f2838fe1daf1626f917090bee3d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB/bundle.json","state_url":"https://pith.science/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB/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":"2026-06-25T11:21:32Z","links":{"resolver":"https://pith.science/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB","bundle":"https://pith.science/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB/bundle.json","state":"https://pith.science/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZ3Y2DWMI2C6OEEKOORVHE7CZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:IZ3Y2DWMI2C6OEEKOORVHE7CZB","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":"d90a930f3b087b73deb2c41b3527d65628c0313de9734008f4ec9240fe7bd4f3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-03-05T12:02:38Z","title_canon_sha256":"8b7e178b6722da176c5f2e0d50d4410c716e5c04eb7243d3cc5eec04b6d45f55"},"schema_version":"1.0","source":{"id":"0803.0640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.0640","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"0803.0640v2","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.0640","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"IZ3Y2DWMI2C6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"IZ3Y2DWMI2C6OEEK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"IZ3Y2DWM","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:f3b3e8f1ff4425c858d5478932b2b376ad84f2838fe1daf1626f917090bee3d7","target":"graph","created_at":"2026-05-18T04:17:13Z","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 define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metric graphs in an easy way and we discuss the behaviour of stretching factors under iterations of automorphisms. We study metric properties of folding paths, showing that they are geodesic for the non-symm","authors_text":"Armando Martino, Stefano Francaviglia","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-03-05T12:02:38Z","title":"Metric properties of Outer Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.0640","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":"sha256:068d166f44f1ffe69fa7e812f4e5f1b4b5270527bf2274b539c7a6c480a7d306","target":"record","created_at":"2026-05-18T04:17:13Z","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":"d90a930f3b087b73deb2c41b3527d65628c0313de9734008f4ec9240fe7bd4f3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-03-05T12:02:38Z","title_canon_sha256":"8b7e178b6722da176c5f2e0d50d4410c716e5c04eb7243d3cc5eec04b6d45f55"},"schema_version":"1.0","source":{"id":"0803.0640","kind":"arxiv","version":2}},"canonical_sha256":"46778d0ecc4685e7108a73a35393e2c879705fe61425a65a5925a41b57d7fe22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46778d0ecc4685e7108a73a35393e2c879705fe61425a65a5925a41b57d7fe22","first_computed_at":"2026-05-18T04:17:13.883567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:13.883567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+DndSrQWRdTmCX4t3r5OYeIy3bdGBVLmTT+ZsYDCNS0cursnpXJq653T5kjI3DuKeIjZeP+ub1DlyJgd1zeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:13.884003Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.0640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:068d166f44f1ffe69fa7e812f4e5f1b4b5270527bf2274b539c7a6c480a7d306","sha256:f3b3e8f1ff4425c858d5478932b2b376ad84f2838fe1daf1626f917090bee3d7"],"state_sha256":"065cf769a9f876e665cf04a99e66d78c38fd206f2e02d66fa894def77201f655"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1g8pDhCEyS9C3v6bTSrFbARquhv2+L0knHML0bZHb7hXU8GKY09f+IAP9olwsAZxRM1JJk2hnviUaN2sc+skAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:21:32.082184Z","bundle_sha256":"3b0aaeb24526269993d2a1e07c9f7817c1df9933ed719bfb8a9236d4b9456244"}}