{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FJYX2JKBEDGUCTRMV3A7VYLTNG","short_pith_number":"pith:FJYX2JKB","canonical_record":{"source":{"id":"1503.02338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-08T22:53:41Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"5752ef7a450e6efe50e369adfb068a31b6d6274997c42ff9d8aa520dfec7548a","abstract_canon_sha256":"3ededbbde46fcf14f95c4ba7748d1695377e9183cfdbf805e89b1956516759af"},"schema_version":"1.0"},"canonical_sha256":"2a717d254120cd414e2caec1fae17369a2a39a4dc3f4a7316653e7bf837501d9","source":{"kind":"arxiv","id":"1503.02338","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02338","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02338v2","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02338","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"FJYX2JKBEDGU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FJYX2JKBEDGUCTRM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FJYX2JKB","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FJYX2JKBEDGUCTRMV3A7VYLTNG","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-08T22:53:41Z","cross_cats_sorted":["math.CO","math.MP"],"title_canon_sha256":"5752ef7a450e6efe50e369adfb068a31b6d6274997c42ff9d8aa520dfec7548a","abstract_canon_sha256":"3ededbbde46fcf14f95c4ba7748d1695377e9183cfdbf805e89b1956516759af"},"schema_version":"1.0"},"canonical_sha256":"2a717d254120cd414e2caec1fae17369a2a39a4dc3f4a7316653e7bf837501d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:08.142961Z","signature_b64":"tkso80TnIci/EZYusqklJz34zoml0K0MMgSgjdOSWSLZZOIY6Shek6QmyLsex/+shk1c4sEnQyqhtekkhgi1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a717d254120cd414e2caec1fae17369a2a39a4dc3f4a7316653e7bf837501d9","last_reissued_at":"2026-05-18T01:32:08.142253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:08.142253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02338","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":"2026-05-18T01:32:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sAj/fa8oLhVMYaJ09tru4EKq2cLpbWqoQ11Bc6BJvclNHBxpWRtzGAsqrxE9QEMcm95BNW/smuxguqxlFwz2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:57:25.014429Z"},"content_sha256":"3546067108986c24109b656f173b9b6b4b11cab32ea671e3d372af3618786ee7","schema_version":"1.0","event_id":"sha256:3546067108986c24109b656f173b9b6b4b11cab32ea671e3d372af3618786ee7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FJYX2JKBEDGUCTRMV3A7VYLTNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster and virial expansions for the multi-species Tonks gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Sabine Jansen","submitted_at":"2015-03-08T22:53:41Z","abstract_excerpt":"We consider a mixture of non-overlapping rods of different lengths $\\ell_k$ moving in $\\mathbb{R}$ or $\\mathbb{Z}$. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities $z_k$ and the densities $\\rho_k$. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-ove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02338","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":"2026-05-18T01:32:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GIrnPxuDoeYGje8cRl5wOv31A9jNxHg3eoyGghs55isMt2Ppk+Plaxsbikq+QGozqZ/hine4bvCYTgBX9rFZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:57:25.014794Z"},"content_sha256":"08ed20632f5bc20e2eae43973d4ce702f4b07d65f84b77a58a31c79b5269eb46","schema_version":"1.0","event_id":"sha256:08ed20632f5bc20e2eae43973d4ce702f4b07d65f84b77a58a31c79b5269eb46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG/bundle.json","state_url":"https://pith.science/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG/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":"2026-06-03T09:57:25Z","links":{"resolver":"https://pith.science/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG","bundle":"https://pith.science/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG/bundle.json","state":"https://pith.science/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FJYX2JKBEDGUCTRMV3A7VYLTNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FJYX2JKBEDGUCTRMV3A7VYLTNG","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":"3ededbbde46fcf14f95c4ba7748d1695377e9183cfdbf805e89b1956516759af","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-08T22:53:41Z","title_canon_sha256":"5752ef7a450e6efe50e369adfb068a31b6d6274997c42ff9d8aa520dfec7548a"},"schema_version":"1.0","source":{"id":"1503.02338","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02338","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02338v2","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02338","created_at":"2026-05-18T01:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"FJYX2JKBEDGU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FJYX2JKBEDGUCTRM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FJYX2JKB","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:08ed20632f5bc20e2eae43973d4ce702f4b07d65f84b77a58a31c79b5269eb46","target":"graph","created_at":"2026-05-18T01:32:08Z","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 consider a mixture of non-overlapping rods of different lengths $\\ell_k$ moving in $\\mathbb{R}$ or $\\mathbb{Z}$. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities $z_k$ and the densities $\\rho_k$. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-ove","authors_text":"Sabine Jansen","cross_cats":["math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-08T22:53:41Z","title":"Cluster and virial expansions for the multi-species Tonks gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02338","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":"sha256:3546067108986c24109b656f173b9b6b4b11cab32ea671e3d372af3618786ee7","target":"record","created_at":"2026-05-18T01:32:08Z","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":"3ededbbde46fcf14f95c4ba7748d1695377e9183cfdbf805e89b1956516759af","cross_cats_sorted":["math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-08T22:53:41Z","title_canon_sha256":"5752ef7a450e6efe50e369adfb068a31b6d6274997c42ff9d8aa520dfec7548a"},"schema_version":"1.0","source":{"id":"1503.02338","kind":"arxiv","version":2}},"canonical_sha256":"2a717d254120cd414e2caec1fae17369a2a39a4dc3f4a7316653e7bf837501d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a717d254120cd414e2caec1fae17369a2a39a4dc3f4a7316653e7bf837501d9","first_computed_at":"2026-05-18T01:32:08.142253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:08.142253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkso80TnIci/EZYusqklJz34zoml0K0MMgSgjdOSWSLZZOIY6Shek6QmyLsex/+shk1c4sEnQyqhtekkhgi1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:08.142961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02338","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3546067108986c24109b656f173b9b6b4b11cab32ea671e3d372af3618786ee7","sha256:08ed20632f5bc20e2eae43973d4ce702f4b07d65f84b77a58a31c79b5269eb46"],"state_sha256":"e6c0a8cc53eb86ac262057e69aa4f9236556a874ec11df5a317dc3502a0875f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoOy0Pfjclkn8/+SlnV0Putj0OcMak+9+/OcOseRNkWQerD0O+3lyNaunaGw7DC51XbLu6uQxWy31tKqJbRjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:57:25.016729Z","bundle_sha256":"eb3ab0b0366e643247d8d6e895e1f758364dcae9b3dadc3c921158529532ca77"}}